Burning Down

No, they don't belong together, which means one of them is being borrowed from another key. A# major is also known as Bb major, so that may put a different perspective on things in terms of figuring out the key. There are a couple of possibilities, and all of them have chords borrowed from other keys:

a minor: the chords of Am and E7 both fit (I and V). However, the IV chord is generally minor in a minor key - so this particular progression would normally be Am, Cm, E7. So the C chord is borrowed from a related key - C major. Following so far? I'm trying not to be too technical here

The other possibility is Bb major (it's not normally called A# major), but this is a long shot as E is the IV chord, which doesn't normally have a 7th added to it in a standard progression. As well, the C chord should technically be minor because it's a ii chord, and it's rare that the IV would follow ii and then move straight to I and skip V. I don't know... There are a few things happening here.

I'm also thinking that this short progression is actually part of a modulation from one key to another key, or at least a tonicization of another key.

Is there more to this progression? I need some context. I'm going with the idea that it's borrowing a chord or two from a related key, but that particular progression you shared is not long enough for it.

If that's it, then it's an interesting progression no matter what!

I probably over thought this too much lol