Carolina Boy--You quite possibly saw a cougar (or mountain lion, or panther, or painter--whatever name you choose). Your size description fits, but another key question is: Did it have a long tail?
Wildlfie biologists consistently deny the presence of panthers anywhere in the Southeast except Florida, yet there have been credible sightings by Park employees, a cousin of mine who is a national wildlife refuge manager in Florida (but grew up in the Smokies and saw the cat there), and plenty of folks from the general populace.
Yet the consistent explanation (or denial) from wildlife authorities is that they didn't really see what they saw or that the animal is a pet which has been released to the wild.
In my personal opinion, and it comes from someone who is not a wildlife biologist but who has read a good deal on the subject of the big cats and even eaten panther backstrap (now there's a novel foodstuff--it was a favorite of the mountain men and is a delicious white meat), I think it quite likely a few of the cats exist in the Smokies. Years ago I heard a sound on the headwaters of Deep Creek which, if it wasn't a panther screaming was either a woman in her death throes or I'm delusional.
Have you notified Park authorities? It would be interesting to see what they have to say.