My first guess would be that you need to adjust the intonation on just the E string.

Play the harmonic at the 12th fret, and then fret the string at the same place. If the notes are not the same, the bridge saddle for that string must be moved closer to the neck, or further away, until the notes match.

I described truss rod adjustment in an earlier post (called "truss rod") in this section. That is something I don't recommend for beginners. If you had a junk guitar that you could cheerfully trash, that's very different from risking your 'one and only'!