The short answer
Hydrogen sulfide in the water causes the smell; if it's only in hot water, the water heater is the likely source. Air-injection and catalytic filters are sold for it.
Find the source
- Smell on hot and cold taps: likely in the water itself.
- Only on hot: often the water heater's anode reacting with the water.
- Test the water to confirm.
Treatment
Air-injection filters: iSpring WCFM400K Air-Injection Iron Filter, AFWFilters AIG15-25SXT-34 Air Injection Gold Fleck 2510SXT Air-Injection Iron Filter. Whole-house sulfur filters and catalytic media are also sold for it; match the maker's limits to your test.
Softeners and sulfur
A softener alone doesn't treat hydrogen sulfide; filter first, then soften.
Products mentioned
Questions readers ask
Will a water softener remove sulfur smell?
No; use a filter made for hydrogen sulfide ahead of the softener.
Why does only my hot water smell like eggs?
Often the water heater; the cold supply may be fine.