The trick of substituting major chords for the same note's minor (and the same in reverse) is a common effect, and can be used to add variety to songs with may verses. Not knowing the song, I can't be sure, but do you know the the song IS in E, rather than just starting / finishing on it? The other chords make a regular 3-chord trick in G, of which Em is its "relative minor" (= the minor key sharing the same key signature as the major key it's "relative" to). The relative-minor-switch might be happening here, especially if the song doesn't actually start on its "tonic" chord.
To achieve the pattern I originally mentioned, try "Big Yellow Taxi" by replacing each chord with its relative minor (3 frets down, and in minor, so C becomes Am). That's one example where the entire verse can work in substitution (it doesn't sound right with every song).