て敵わない means "it's so ~ I can't stand it". It goes after the て-form: くて for an い-adjective, で for a な-adjective, the て-form for a verb. The speaker is complaining about something they are putting up with.
、。
It's far from the station, and it's more inconvenient than I can stand.
。
Being made to work overtime every day is more than I can take.
is "to be a match for", so the sense is that the heat or the noise is more than you can take on. It is usually written in hiragana, てかなわない.
てかなわない or てたまらない
and
say a feeling is too strong to hold in, and the feeling can be a happy one. てかなわない is only for something you find a nuisance.
。
I can't wait to see you.
。
The neighbor's dog has been barking since morning and I can't bear it.
Register
It describes your own discomfort; for someone else's, add or . It is heard in speech as well as read, but it has an older ring to it. The everyday way to say the same thing is てたまらない or てしょうがない.
。
Apparently my father can't stand the noise from the construction next door.
Lingaku