That's what I mean by chord structures. To play an E7 all you need to do is flatten the 7th note 1/2 step from the Major voicing. (Don't ask why they call it E7 and don't emphasize flattening the 7th interval. It is known as dominant 7th. If the 7th is not flattened that chord is noted as Emaj7 and that is the only difference).
To make sense of this, the E Major chord is constructed using the 1st(root) note(E), the third note(G#) and the fifth note(B) of the E Major scale. That's it, three notes out of seven.
The E Major scale (doe-rey-me-fa-so-la-tee-doe) consists of the notes
E-F#-G#-A-B-C#-D# and starts again with E(doe). D#(D Sharp) is the seventh note. To play E7 you have flatten (lower) D# 1/2 step down which now becomes D and add it to E (root), G# (third) and B (fifth) Major chord. Here is an E Major chord in open position (three notes E,G# and B)
e|------|-------|open
b|------|-------|open
g|-G#--|-------|
d|------|--E----|
a|------|--B----|
E|------|-------|open

Here is an open E7 (four notes E,G#,B and D)
e|-----|--------|open
b|-----|--------|open or optional pinky finger @ third fret (D note)
g|-G#-|--------|
d|-----|--------|open
a|-----|---B----|
E|-----|--------|open
All you really need to do is lift your finger off the d string second fret and play it open. Adding the optional D note on the second string will further emphasize the dominant 7th chord.