Eventually I'd like to get so good at this that when I see E7 on the chord sheet for example, that my brain instantly knows E G# B & D...
First of all, know that every key has a key signature. In your example of E, immediately I know there are 4 sharps. (Again... WWHWWWH)
To make ANY 7th, think "UP one octave to the next higher root then move down 2 frets." In any key. Flat the 7th note in the scale.