Watch the E Major online guitar lesson by Brad Carlton from Guitar Lab: Open String Universe
The chord presented in this lesson is the E form in open position. The voicing is as follows from lowest to highest in pitch: Root, 5th, root, 3rd, 5th, root.
There are four common scales(modes) that are applicable to this voicing. They are ionian: 1-2-3-4-5-6-7, lydian: 1-2-3-#4-5-6-7, mixolydian: 1-2-3-4-5-6-b7, and overtone: 1-2-3-#4-5-6-b7.
Notice how the chord tones (1-3-5) constitute a subset of each of these scales. Since the ionian, lydian, mixolydian and overtone scales are in the heptatonic category (seven note scales), there are four color tones available to the soloist. They are the 9(2), 11(4) or #11(#4), 13(6), and 7.
Your scale choice may be clearly defined by how this E chord functions, so analyze the progression you are using it in. If it is functioning as a static chord, consider any other melodic or harmonic parts that may be occuring in the music.