To my ear, the two E chords are a temporary, direct modulation to E major. They take advantage of the root movement from G to F# and also serve to set up the bridge. (Note that jazz and blues allow for the interpretation of a major key even when the minor seventh is present.[1])
In a different context, E might be interpreted as IV borrowed from B major, but while it is literally the case, I don't think it explains the overall sound any better than just thinking in terms of root movement. Similarly, other "standard" explanations, like treating the F#7 as a common-tone chord with E, I think also stretch the theory too far.
[1] Although Jazz, blues, and popular music harmonies are often in line with the common practice model of tonality, the don't adhere strictly to it. The presence of the ♭7 in major is a good example: it is frequently treated as a consonance rather than a dissonance. The bridge of this piece is a perfect example. The underlying harmony is E7, but the whole section is clearly perceived as E major rather than A major, as common practice tonality would demand.