Respectfully suggest checking it in GAS operation before changing the AC element. The Gas Valve has a "One Time ECO" (Energy Cut Off). There's a thermal link in the sensing part of the Gas Valve. Part that pokes into the water tank to determine water temperature and cycle the gas flame. Hopefully the electric element burned out before it got the empty tank hot enough to open the One Time ECO in the Gas Valve.
If it heats water on GAS, that $100+ thermostat is still OK and replacing an inexpensive element should get you running again. If it needs BOTH, you may want to consider your options, particularly if you hire somebody to work on it.