Scales to Play Over Eadd9
Every chord is a subset of several scales: any scale that contains all of a chord's tones fits over it. Pick a chord to see the matching scales from its own root, the major keys the chord belongs to, and full fretboard diagrams for every scale on guitar.
A Eadd9 chord contains the notes E – F# – G# – B. Any scale that includes every one of those 4 tones fits over it — from the root E, that means E Major, E Major Pentatonic, E Rock 'n' Roll, E Lydian, E Mixolydian, E Dorian Bebop and E Mixolydian Bebop. Start with the first scale listed: it is the most common choice, and the others color the same chord tones differently.
Eadd9 is also diatonic to 3 major keys: A major (relative minor F#m), B major (relative minor G#m), E major (relative minor C#m). In a song from one of those keys you can also solo with the key's own major scale or its relative minor pentatonic across the whole progression, not just this chord.