it may very well be an intonation problem. Tune the open E, then check the note on the 12th fret of the E string. if its sharp you may have to push the string saddle of the bridge further away, if its flat you have to move it forward. You will have to really loosen the string to relieve tension enough to get the string saddle to move. So just adjust it just a little bit, then tune the string up and try again. it might take more than one try to get it right, but of course being in tune is worth it. Also, i would make sure all the other strings arent problematic.