White smoke at exhoust and puch water out of the radiator

White smoke is an indicator of moisture. All cars will show water vapor at start up as heating up drives moisture out of the exhaust system AND the combustion of fuel produces water vapor. Until things warm up, slight white "smoke" can be seen coming from the exhaust. If there is a lot of smoke, more than a normal car starting up, that could be radiator fluid leaking into the combustion chamber. Is the radiator fluid level going down? If it is, that it could be a gasket leaking.

Good news and bad news.
All cars & truck with gasoline engine can emit white smoke on start up.
This is water vapor evaporating .
You have a problem if you have white smoke after the engine is warm, unless you are way up north and the outside temperature is really cold.
Also, keep close watch on the radiator to be sure you are not losing radiator coolant ( perhaps a leaking head gasket ) and the motor oil on the dipstick (should not be "milky" or the color of coffee w/cream)
as that could indicate water in the oil, which is really serious.
God bless your efforts.

the main problem caused by white smoke is either steam which is head gasket leaking water into cylinders /and will also have condensation or water out of the rear end exhaust ,or if running ok and no loss of water in radiator and starts ok then could be a mix of fuel .but if you are loosing water then its the first problem.
As if it was oil burning then its black smoke you should have not white.

Borrow a radiator test kit from autozone or buy one fro harbor freight. Pump it up to around 18psi to See if it holds for about an hour. If not you probably have a blown headgasket. If its white smoke...its your coolant being burned in the cylinder and vaped out your exhoust..

That is probably the head gasket leaking. White smoke is from antifreeze going through the exhaust. The engine compression is pushing the water out of the radiator.

white smoke could be head gasket leak. but white smoke will come with warm engine. If engine is first start cold. IT's only water in exhaust system

If you have white smoke coming out of the exhaust after the car warms up then you have coolant getting into the cylinda white smoke after start up when the engine is cold is normal intill everything warms up

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White smoke is usually burnt water.
Check your radiator water level, if it is down, check for a blown head casket in your engine e.g.(water in the engine oil, or oil in the radiator water) brown froth on filler caps.

Sounds like you have blown a head gasket. Do not run the engine like this or you will seize it up . anti freeze will freeze the pistons and you will need a new engine. Hope you have not ruined it now.
White smoke is a sign of water in the piston area.

white smoke means water getting into combuston chamber ,head gasket maybe