My tv has audio output with rca jacks
The subwoofer is not powered, and it has a single rca terminal (can be taken off to have a hot and ground wire
In that case a receiver is your cheapest solution. Other wise it gets complicated. Even then you will need an amp for your sub.
With no receiver you will need a two channel amp that allows you to switch inputs, an electronic crossover and an amp for your sub. That will be complicated and expensive and you will not have the ability to add to your system.
You still did not tell us what your TV is, or a link to the manual. On most flat panel TVs, the analog RCA out shave very limited functionality.
Everything is geared to all the peripherals going to a receiver or pre/pro, with one HDMI connection to the TV.
If you buy a receiver do not buy a cheap one, start at the mid level.