Your TV may have two kinds of audio outputs according to online specs.
First is a 3.5mm stereo headphone output. That would connect directly to the Aux input on the Bose.
Second is an optical audio output. You would need and optical to analog converter like this one
http/www.parts-express.com/parts-express-dac-digital-to-analog-converter-(51-compatible)--180-999
to connect the TV to the Bose.
If there are no outputs of any kind then short of modifying the TV you would need an external HDMI input selector with audio extraction like this one
https/www.monoprice.com/Product?p_id=5557&kpid=105557&gclid=CPPY2sLnwcYCFYIXHwodhY0FTw
This would not work with the TV tuner or smart functions since these are internal to the TV.