The hot water smells like rotten eggs., only the hot water

It is unlikely to be the hot water heater causing the smell, it is more likely the input (the well water) having excess sulfur, bacteria and/or organic material

Because it sits in the tank longer, the smell accumulates. If it is a bacterial source, the hot water tank may be a breeding ground for anerobic bacteria. Draining and doing a disinfect with Hydrogen Peroxide (H2O2) is the easiest and safest step

http://www.waterheaterrescue.com/Troubleshooting/stinky-water-in-hot-water-heaters.html

https://www.stevejenkins.com/blog/2015/02/fix-rotten-egg-smell-in-your-water/

Some water softeners you can increase the back wash time on the unit to clear out a smell or bad taste , rotten egg smell can be sulfur. You may need a well flush but seek a well company on that for there advice as its not cheap .

first replace your anode rod if that doesn't work the problem is in your water look at water treatment systems

Anode rod is reacting with well water
http://waterheatertimer.org/Replace-anode-rod.html#smell
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If you need further help, I’m available over the phone at https://www.6ya.com/expert/gene_9f0ef4df2f9897e7

Clean the tank with hydrogen peroxide as outlined in following link.
You may also need well company to shock-treat the well with clorox, or whatever procedure they recommend for local area.
http://waterheatertimer.org/Replace-anode-rod.html#H2O2

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

Water pressure is blowing everyting loose with new heater,give your system a good flush,it will work it self out. RichieRich

When the water heater smells bad, it is time for a new anode rod.
And then you flush the water heater with 2 bottles of hydrogen peroxide.

With water heaters that experience the problem frequently, you change your incoming cold water pipes so hydrogen peroxide can be added easily.

http://waterheatertimer.org/Replace-anode-rod.html
http://www.thisoldhouse.com/toh/video/0,,20047047,00.html
http://www.waterheaterrescue.com/pages/WHRpages/English/Longevity/water-heater-anodes.html
http://www.prweb.com/releases/2010/02/prweb3592714.htm

You'll have to disconnect the water lines from the top to pull the rod up out from within the tank. If you don't have enough clearance above the tank, you'll have to drain the tank, remove the venting and tilt it or lay it down to remove it. The sacrificial rods usually go bad prematurely on well water systems with hard water and causes a sulfur stench in your water. Here's a quick test to try before you do this: Go to the nearest faucet to the water heater and fill a glass full of cold water and another glass full of hot water and smell them. If the hot water is the only glass that smells like rotten eggs, it's most likely coming from your water heater due to your anode rod. Douglas

Hey check out this link that I found on this matter I hope will help you with this.
http://homerepair.about.com/od/plumbingrepair/ss/trblsht_hwh_5.htm

boiler type? Combi,standard,if your boiler is a combi the non return valve onto your heating line may be defective thus hot water slippng back through cold line best of luck