The E major scale family has the C#m, G#m and B major (the Vth) chords.
This song brings in the C major chord, G major chord etc into the harmony in a smooth and easy manner through the melody.
Below are the chords of the song based on the phrases. These are different at least partially, from the chords used in the original recording. The aim has been to find suitable chords based on the phrases, the melody notes.
The chord chart is below is the video