tldr: Straightforward chords, but with some ambiguity as to the tonic. I characterize this song as primarily E mixolydian, but the Bm chord that opens the main progression gives a flavor of B minor (dorian). The chorus could be characterized in the same key, but I think there is a subtle shift to A major. There is also a short bridge in D major that includes the only borrowed chord in the song, an E major II chord, which pivots back to the E mixolydian parts.
Like Sugaree, this song is simple to play, but less simple to explain (at least for me). The reason is that the chords fit within a few different keys without definitively establishing which one is the tonal center. E mixolydian, B dorian, and A major all have the exact same notes and diatonic chords; the difference is which chord serves as the tonic, and sometimes that can be hard to identify. The bright side is that it’s purely academic here — it doesn’t really change how you play the song.
Is it B dorian? The main Bm – A – E progression that serves as intro and verse starts with a Bm chord, which, I think, gives the song a minor feel to it. This arguably suggests B minor as the key, with a i – bVII – IV pattern. And the major IV chord (instead of a minor iv) would signal the dorian mode.
Is it E mixolydian? Although the main progression starts with Bm, it firmly ends on E, as does the entire song. If E major is the tonal center, the chords Bm – A – E fit perfectly within the mixolydian mode as a simple v – IV – I progression.
What about A major? Although the main progression isn’t in A major, based on the small role of the A chord moving between the Bm and E chords, there is arguably a shift to A major in the chorus. (I’m calling this part a chorus because I’m not sure what else to call it). The progression of A – Cm – D – A, Cm – E would be I – iii – IV – I, iii – V from the perspective of A major.
I resolve these competing thoughts by focusing what I think is the cleanest explanation from the practical standpoint of playing the guitar. And that is a v – IV – I in E mixolydian for the intro and verses and I – iii- IV in A major for the chorus. But it is subjective, and you may reasonably disagree.
The solo is based in chord tones, but the notes all come from the E mixolydian/B dorian scales (which are identical), depending on what key you identify the song as residing within.
Finally, there is a bridge of D – G – E. You could view this progression within the context of one of the other keys, but it sounds to me like a key change to D major, with the D and G creating a I – IV sound, and the E chord borrowed from D Lydian, which is yet another scale identical to E mixolydian/B doran/A major. Again, this is more subjective than usual and you may reasonably disagree.