The pentatonic scale is a simplified version of the minor scale.

E major and E minor can not work at the same time in theory. Pratically It might sound good. However you can not have a minor 3rd and a major 3rd in the same scale. You can have a minor 3rd and a diminished 4th, or a major third and a 4th but not a minor third and a major third. Scales containing a diminished 4th would not include diatonic major scales or their relative minors.

An E major chord is built from a major 3rd and a perfect 5th. These notes happen to be in the E major scale also. An E minor chord is built from a minor 3rd and a perfect 5th. These notes happen to be in the G major scale also.

Since E major contains notes from the E major scale and E min pentatonic contains notes from the G major scale they dont really work together. If you try to play them in harmony someone is playing in a different key.

Every major scale has a relative minor. The 6th step of the major scale is the tonic to its relative minor scale. All natural minor scales and major scales are relative to each other. C major = A minor, G major = E minor, D major = B minor, ect...