"Smelly rotten egg" water is created when hydrogen sulfide gas is formed in water. As water warms, the hydrogen sulfide is released into the air above the water with a characteristic "rotten egg" smell.
Fortunately, sulfur filters can resolve this problem!
By far the best "sulfur filter" system we've found is the Oxidizer Plus+ from Addie Water Systems, Inc. based in Janesville, Wisconsin. This unit aerates and oxygenates "smelly water" by spraying water through a compressed bubble of air in an enclosed tank. The spray increases water's surface area and enhances the dissolving of air (and oxygen). The increased surface area enhances oxygenation of hydrogen sulfide into sulfuric acid. These compounds both acidify the water and lower the pH. The lowered pH has the added benefit of increasing the solubility of ferric (iron) acids in hard water, and providing a "clearer" solution to reduce water stain.