Water leak from top of hot water tank ?

Gas or electric?
Electric water heater ... then test for crossover, check for water leak, replace thermostats, test elements
Gas water heater ... test for crossover, check for water leak
http://waterheatertimer.org/Crossover.html

http://waterheatertimer.org/How-to-replace-thermostat-on-electric-water-heater.html

http://waterheatertimer.org/How-to-test-water-heater-element.html

water leak: turn off all taps and put ear against pipe and listen for water leak... check if water meter advances when all water taps are off.

Gene

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Emergency steps:
Turn electric power off.
Release tank pressure by opening bathtub faucet on hot side.
Turn off water supply to heater.
You can turn water heater ON for short periods (1/2 hour) to make some hot water until repairs are made.

It sounds like runaway heating caused by shorted element, possibly caused by leaking water. But I cannot tell for certain what the problem is. Read following links and/or call plumber.
http://waterheatertimer.org/Leaking-water-heater.html
http://waterheatertimer.org/How-to-troubleshoot-electric-problems-with-water-heater.html

Over-amping:
Look at watt rating label on side of tank.
For example 4500 watt water heater requires 30 amp breaker and 10 gauge wire.
If you have 20 amp breaker and 12 gauge wire, then change elements to max 3800 watts. Tank will heat more slowly.

You have to fix leaks, and I cannot see that problem. Call plumber or repost question with clear description of leak.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Yes, turn off leaking water heater because it might rupture.

Sounds like the tank is rusted and needs to be replaced.
Open following link:
http://waterheatertimer.org/Leaking-water-heater.html

For your next water heater, read following information
http://waterheatertimer.org/Replace-anode-rod.html
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

Upvote the help.
And take advantage of fixya expert assistance live.
For a price, expert works with you while you work on water heater or any do-it-yourself project.
Fixya is always less expensive than a service call.

Have you tried it with both (hot rod and Gas ) turned on at same time? Is tank well insulated? (looking from behind tank.)
Does temperature drop off quickly, or gradually? Did it supply hot water better before, or this is first time you really measured it out? Need to keep in mind that as hot goes out the top fitting to hot lines, cold is coming in the bottom fitting and beginning to mix with hot, which obvioulsy will cause hot to gradually become warm as it enters. 2 gallons out hot tap, 2 gals., at bottom of tank, then mixing as it flows in usually equals, about 2 gal or less of warm, then cold again. Get many complaints of only enough for a short shower when they have 6 gal tank. You can try adjusting temperature up a little to see if it helps. Keep an eye on pressure relief valve dripping excessively as well as shut pump off for 20min-30 min, then turn it back on before touching any taps, to see if it cycles at all, indicating a leak in the system. If pump doesn't cycle when turned back on, no leaks.

Your tank is rusted out and needs to be replaced.
Link below is a troubleshoot for leaking water heater.
http://waterheatertimer.org/Leaking-water-heater.html

Protect yourself first:
If your tank is rusted, there is danger of rupture.
My friend welded his leaking tank, but he assumes the risk.
Ruptured tank can cause massive damage and water runs until it is shut off.

Hot water tank is under pressure because hot water expands and pushes against tank wall.
Turn off water to tank.
Turn off power supply:
Electric: turn off circuit breaker.
Gas: rotate knob to pilot so pilot stays lit but burner will not fire. To turn back on, rotate knob to ON.
Open hot side bathtub valve and relieve pressure on tank.

You can limp by with rusted tank by turning water heater on when hot water is needed.
Shower uses 5-9 gallons hot water
Bath uses 12-15 gallon hot water
Ordinary gas heater makes 41 gallons hot water per hour
Ordinary electric heater makes 20 gallons hot water per hour.

I buy water heaters at Lowes, Home Depot, Ace.
Look for scratch and dent models.
Buy drip pan for water heater.
Wrap electric heater totally with insulation except TP valve.
Buy new flexible connectors for water lines.
Offer 15% less than marked price on tank, because the store makes money on additional items.

> Most people can install their own electric heater since you just connect water pipes and electric wire, and it's done. Read link below since there are tips that help you buy and install electric.
> Generally people are nervous about installing gas water heater, so step-by-step instructions are shown on link below. Remember gas line is under less pressure than water line, so if you can install a water pipe, you can install gas line to water heater with crescent wrench, and soapy water to check for leaks.
How to install gas water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html

Add a comment for more free help.
Also take advantage of fixya phone service.
For a price, fixya expert speaks with you over phone while you work on water heater, or any do-it-yourself project.

A leaking water heater cannot be repaired, assuming it's the tank leaking and not nearby water pipe.
http://waterheatertimer.org/Water-heater-leaking.html

First thing is to protect your property from catastrophic tank failure where tank ruptures and water runs until it is shut off:
Tanks are under pressure when they are hot.
Close cold water shut-off located above tank.
Turn control knob to 'pilot' so pilot is lit but burner will not turn on.
Open hot side on tub for few moments to relieve tank pressure.

Now your property is safe.
You need a new water heater.
In mean time, gas water heater makes 41 gallons hot water per hour.
Shower used 5-9 gallons hot water.
Bath uses 10-15 gallons hot water.
You can turn on water heater for short stretches and limp by until you get a new heater.

Steps for installing gas water heater:
http://waterheatertimer.org/How-to-install-gas-water-heater.html

I wrote a page on leaking water heaters with resources and information:
Page lists things to check.
http://waterheatertimer.org/Water-at-bottom-of-water-heater.html

Also run hand over tank to find warm spot that says where leak is coming from
A rusted tank cannot be repaired.

If your tank is rusted out, it might burst open and flood the area.
Hot water inside tank is under pressure.
Turn off heat source to water heater.
Turn off water valve located above tank.
Open tub faucet on hot side and relieve pressure from tank.

You can limp along with a leaking water heater by turning it on when hot water is needed.
For example a shower uses 5-9 gallons hot water.
Turn gas water heater on for 15-20 minutes.
Turn electric on for 20-30 minutes.

To conserve resources with next heater:
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html

I wrote a page on leaking water heaters.
With a checklist.
It sounds like you've done quite a bit already.
The element can leak around the gasket.
The TP valve can leak where it screws into side of tank.
Otherwise a leak on side of tank sounds like the tank is rusted through and needs to be replaced.
http://waterheatertimer.org/Water-heater-leaking.html

You should turn off electricity and water to the tank, and open tub valve on hot side to relieve pressure so the tank will not rupture.
Then you can limp along with a failed water heater by turning the water and electricity on only when hot water is needed.
This will buy you time until a new heater is installed.
A typical electric water heater produces 21 gallons of hot water per hour.
A shower uses 6-9 gallon of hot water, so heater only needs to be turned on 20-30 minutes for a shower, more if the incoming water is very cold.

To economize with your next heater, you might read the following two pages:
http://waterheatertimer.org/9-ways-to-save-with-water-heater.html
http://waterheatertimer.org/Replace-anode-rod.html

Turn off the electricity.
Turn off the water valve going into tank.
Open a bathtub spout to let hot water pressure off the tank.
Check top of tank for any leaks.
Open the top access panel and see if element is leaking.
Open bottom access panel and see if lower element is leaking.
The reduced pressure on the tank will slow the leak.

If element is the problem, you can squeak by for a while by turning on the hot water heater only when you need hot water.
Order the 'Marathon MR85245 replacement element' online
http://www.gpconservation.com/rheem/marathon-sp213670-titanium-4500w-lower-element
These elements may be available locally, but they are not the same as 'ordinary' tank-type electric heater elements that you buy at the hardware store.
Buy more than 1 element because the Marathon elements have problems.
One of the reported problems with marathon elements is the high price of stainless steel replacement elements.
Drain tank.
Replace element.

Another resource for water heater information is:
http://www.thetankatwaterheaterrescue.com/forums/forum3/

It could be back flowing into the hot water heater tank which is not full because of the leak. Even though the valve is closed on the cold water entry side, there is probably no valve on the exit side. That is how it is returning to the tank.