Oh gee never mind you're completely clean
Uh, you know that isn't a violation of the TOS, right? Half of all Steam games come with cheats. I can't get VAC banned for giving myself gold in Skyrim, dummy.
Valve does lift VAC bans. Although it's clearly too late now, it's possible they would have lifted if you explained the situation.
Well, I did contact them. I was told that even though I wasn't using 'hacking software' it was still a violation of the TOS to have it. Cheat Engine isn't hacking software...