Both state detours are going to suck! Those roads are curvy and everyone is going to be going that way. Trust me I ride motorcycles up there all the time. Stay away!!!!!
To get to Knoxville TN take 25E in Corbin KY down to Hwy 33 in Tazewell. Follow 33 into Knoxville.
If heading to NC. Get off 75 in Corbin KY and take 25E to interstate 81 south. Then back onto interstate 40 east.
If going to west side of Knoxville take hwy 92 in Williamsburg KY to Hwy 27 south. Follow 27 south to Wartburg TN. In wartburg take 62 south into Oak Ridge. Through Oak Ridge to HWY 162 that will drop you back on 75 south on the west side of Knoxville.
These directions are way better than going the states detours! Check it out on a map!!