Seems a little wonky...
If temp is set at 120 it should not be at 160 out of faucet, that will burn.
And relief valve should not vent unless something is wrong and having too high a temp or too high a pressure are the reasons.
If the element went bad maybe the thermostat in the tank went bad too and is not controlling temp like it should and might need to be replaced too.
Worst case an electric water heater is the cheapest to replace and might be the best option if the high temps and venting continues.
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