What type of TV? There is still not enough information to tell since we don't know what type of batteries however, lights and some TV / Water pump use should be fine each night.
The only time I have done real dry camping was in a TT once and that was here in Florida in the dead of august. We ran a generator right up till quiet time with the AC turned down all the way to get as cold as possible. Then we turned the genny off and plugged a small inverter in with a power strip and extension cords. We ran a pair of small fans and a TV from the inverter and the usual non-led lights and light water pump use. The fans and the amber light outside above the entry door ran all night. Usually around 1 or 2 am, I would wake up uncomfortable due to the humidity and open the roof vents which made it fine till morning. We only had a single 3 year old dual purpose (Non-Deep cycle) group 24 battery and it did fine every night.