The headphone jack on the TE is pretty much the standard stereo mini-phone jack, albiet a cheap one.
It contains two independent sets of "springy" switching contacts, one for left and one for right.
Without the 'phone plugged in, the switches connect their respective L and R inputs straight through to their L and R outputs. And, since there is obviously only on speaker on the TE, those two output are connected together to feed the speaker.
When the 'phones ARE plugged in, the switches are mechanically forced into their opposite state, which disconnects the two outputs from the speaker, and routes it to the L and R channels on the 'phones.
Given your symptoms, I would suppect the two switches have failed; either they have lost their springy-ness, or have broken off completely due to repeated movement. The buzz you hear is the result of having the ground circuit, and only the ground circuit, being connected the the 'phones (the L and R circuits are NOT connected). The unconnected L and R 'phone lines act as sort of an antenna, and pick up the inherent noise in the TE's other circuits.
The 'phone jack is almost impossible to fix; even if you bend the switches back to their original position (assuming they have not broken off), they will only fail after again one or two more uses. Replacing the jack is the best option. Finding one, however...
Charlie