No greater money will be made over a home game. I think the Knoxville area will lose money (restaurants, hotels, parking, etc) compared to what little UT is going to get paid for the Bristol event.
Was looking at the economic impact study from ten years ago and each home game brought in $3 million dollars not counting ticket sales of another $3 million, concessions $343,000 and parking fee income that was not listed.
Yes, attendance is not as good as it was ten years ago but there is no advantage for UT to play the game at Bristol other than publicity. Considering all things money will be lost compared to if the game were played here.