I own a house with an electric GE hot water heater. 8ESOT12AA01 Serial # 090122 5750 I do not know how old the hot water heater is and advice about when it should be replaced. No leaks to date but I don't want to flood my house.

GE is made by Rheem, but the market is always changing. Rheem-based serial number shows tank was made in 1990.
Tank will last as long as anode rod(s) protects steel tank from rusting.
If your tank has two anode rods, then tanks lasts longer.
That's how companies determine if water heater is '6-year' or '12-year.'
I don't have manual for your product to say if you have 12 year tank. Side of tank might have information blurb besides mandatory label that shows serial number.
You can update your water heater by replacing anode rod(s) assuming they can be loosened and removed after this number of years, which is a big IF with old heaters. Your plumber might have impact wrench he uses to see if anode can come out.
http://waterheatertimer.org/Replace-anode-rod.html
http://waterheatertimer.org/Leaking-water-heater.html

If the water heater is making gurgling rumbling and/or crackling sounds then tank has sediment build-up.
You can also get a baseline of rust by flushing tank and watching if water is very rusty.
http://waterheatertimer.org/Clean-sediment-out-of-water-heater.html
http://waterheatertimer.org/Water-heater-will-not-drain.html

If you flush tank regularly, and inspect anode every 1-3 years, a tank will last many years longer than manufacturer's label.
http://waterheatertimer.org/Water-heater-manufacturers.html