Thanks for the question. The SoundTouch 300 isn't able to accept a headphones connection, as the Bluetooth that's built into it is only a receiver, and not a transmitter. This means you can only send audio to the Soundtouch 300, and cannot send audio out of the SoundTouch 300 to something else.
What you might be able to do is connect a pair of Bluetooth headphones directly to your television. What Brand/Model TV do you have? Do you know if it has Bluetooth built in?