I agree with Tim's
D6sus2 suggestion, but I thought I'd add to the entire progression:
Am F G C F X E E7
We begin in A minor; that's clear enough.
But after this, there's a brief move towards the relative major; the
F G C is really just a IV-V-I in C major.
Then we end up moving back to A minor (if we ever left). The
F chord is VI, and the
E7 are just V moving to V7.
As such, it's best to understand the
X as something that connects VI to V. Ideally, this would be a predominant of some kind, and one of the most common predominants is
IV. Sure enough, the reading of
D6sus2 is in fact a
I like this better than reading it as an inversion of
E7, and for two (and a half) reasons. First, it's relatively uncommon for a seventh chord to lose its chordal seventh, and then adding it back again is even more strange. Furthermore, with D in the bass of this
X chord, our ears will tend to view that as the root.
The half a reason is a bit speculative: by reading it as a type of D chord, you have a IV-V at the end, which mirrors the IV-V-I you had in C towards the start of the progression. (You may think that's finding patterns where there really aren't any, and I wouldn't really disagree.)