[jjk166]

Vaporizing at 18 C produces vapor at 18 C, vaporizing at 100 C produces vapor at 100 C. Once you account for cooling the vapor back down to ambient temperature (specific heat pretty close to constant varying from 1.86 to 1.89 kJ/(kg.K) from 18 to 100 C) you get the same amount.

You use the cold incoming water to condense the hot vapor, thus pre-heating it prior to distillation. You get out all the heat you put in, the issue is that vapor has higher entropy than liquid water so you can't use that heat efficiently enough to vaporize the same quantity of water. That's in the efficiency term we are handwaving away.