Distance: 520 mi or about 8 hours 36 minutes, according to Google Maps.
If you need gas, the Citgo at Exit 150A (Troutville) usually has the lowest prices in the Roanoke area while Wytheville (Exit 77, another Citgo) is a good place to stop closer to TN. There is a new Sheetz at Exit 70; it has nice restrooms, the gas should be competitive.

End at Carnegie Hotel
1216 W State of Franklin Rd, Johnson City, TN 37604
You can either take the route shown in blue on this map (Exit 23 Main St (old exit 32)) or go to the Exit 24 and follow the Carnegie Hotel road signs (see next section).
Anyone coming in I-26 from north Carolina should use Exit 24 (below).
The Carnegie sends people around University Parkway (the yellow road towards the bottom of the image). University parkway is a 2 lane divided highway and while it's longer, you definitely won't get lost or make a wrong turn going that way. Just follow the signs to East Tenn. State (ETSU) - the hotel is across the street from the campus.
The reception is downtown, but its not marked on this map.