There are several ways...A Track Volume Envelope, inserted at the Clips pane in the track view. allows you to place dots on the line and lower the volume off at points where you have the noise in blank areas of the track. However when you insert an envelope it is there and does not allow you to use the fader in the mix area of the tune.
I prefer to just do a "Split" on the track, right before the solo, and right after the solo. Highlight the track or tracks you want to split, right click and "Split", the track. Then highlight, right click, and "Cut" the areas where you want silence. Afterwards, you can then fine tune by dragging the track to the first and last note of the solo. If for some reason you want this to be a full length track even with the blank areas? After you cut all the unwanted areas out of the track, Bounce it to a new track, and that will fix that. This method doesn't invlove having the envelope control the fader.
The Gate in the Master Pane of the TH2 can help a bit, but as mentioned it is a hard gate and can interrupt the effect if not carefully adjusted.