is this your tv?
http

/westinghousedigital.com/products/led/32-40/dw39f1y1/
Output SPDIF Digital Audio (Coaxial) 1
Output Audio Out 1
do you have either of these spdif output options? one looks like an orange rca port the other looks like a semi rectangular port with a dust flap.
if you do have those ports you could use that as an output and then use something like a spdif coax to rca adapter (which would have a DAC built in) then use a rca to headphone adapter (or some of those boxes have a headphone port right on them.. perhaps search for spdif coax or spdif optical to headphone dac)
if you dont have those ports then say so.