On an Origin controlled Patch 1.69 game, there is supposed to be a way to move the install from within Origin. It reportedly works around half the time for TS3 games. On a 1.67 disc or I think Steam install, the only way is to uninstall, clean the Windows registry, and reinstall onto a user defined sub-folder on E.
Independent of the program install is the TS3 user game folder in Documents. One way to shift that to another drive doesn't involve re-installs, but rather instructing Windows to redirect the Documents (or My Documents) library entirely to E. This is for Win 10, but the procedure is about the same for other versions.
https://www.dummies.com/computers/operating-systems/windows-10/how-to-change-the-location-of-user-folders-in-windows-10
If one wants to keep Documents itself on C but shift the TS3 user game folder only, then what we call symbolic links or junction points would be required.
Is your C drive an SSD and how large is it overall? While one generally does need more than 35 GB of free space for Windows and the game to manuever properly and for sanity's sake, the benefits of running off of an SSD get lost if either portion of the game is moved to a regular, slower HDD. The game itself will play about the same either way, but on an SSD startups, saves, travel transitions, caching, catalog building in Build/Buy, CAS, and CASt patterns will go very much faster. If C is indeed an SSD and happens to be larger than 256 GB, perhaps there is another way to free up some space and keep it that way. But if this is the PC you
posted about here last year, then it has a 128 GB (showing up as 120 GB) C drive that is indeed far too small to be running games like this one alongside of Windows. SSDs that small are intended for the operating system and related processes only, and are not really for other program installs.