This is from A mighty fortress is our God. How do we explain the E major chord in this progression? The tune is in C major. The melody in this part of tune sounds a bit minor rather than major to me.
There's a few ways to justify this E major chord.
We could notice that the NEXT chord is Am. (Lucky you didn't QUITE cut it off - it's always better to show more context rather than less in this sort of question.) Nothing unusual about a modulation to A minor from C major, and nothing unusual in approaching a new key through its dominant.
But that E chord COULD have been the final ending. Jazz Theory would call it a 'Chromatic Mediant', but resting on III (or on VI) goes back well into Common Practice. I expect there's a name for it.
This phrase of the chorale is in A minor, so the E major chord is just a normal V chord in the new key, creating a standard half cadence in the relative minor. It’s always possible to debate whether to call something a modulation or just a brief tonicization (in which case the E major chord would be called an “applied” or “secondary” dominant and would be labeled V/vi), but in this case I think it’s pretty definitively a full-fledged modulation. I say this because it’s a cadence, and because the preceding harmonies include pre-dominant functions in the new key.
Still, the most important thing to understand is that the E major chord is basically functioning as the dominant of the relative minor.
In chorales you want to look at all those fermatas and rests and identify the cadences.
It doesn't really matter if you label the various phrases as modulations or temporary tonicizations. Chorales often move quickly to different tonal centers from phrase to phrase.
I can't see all the score, but it looks like there are two phrases ending in half cadences in
C major. After the second cadence the harmony goes:
C: I vi iii(Am:v) Am: i6 iv V. Someone might quibble about which chord is the "pivot chord" but it doesn't matter.
The important thing is that the phrase ends with
Am: i6 iv V which is a half cadence.
Structurally, this kind of thing happens a lot. Phrases ending in half cadences in changing tonal centers.
I wish you had included more of the score so we could see the next phrase. It wouldn't be unusual for the next phrase to end in yet another key. The reason this matters is because it would demonstrate that a half cadence alone is enough to define a tonal change. In other words the phrase after this
E major chord does not need to continue in
A minor was already reached with the half cadence.