Which notes harmonize with E and what might be a good note to play outside of the key of E for a dissonant effect?
The notes that harmonize with the key of E major are:

-   E - the tonic or keynote
-   G# - the major 3rd above E
-   B - the perfect 5th above E
-   D# - the major 7th above E

To achieve a dissonant, outside-the-key effect, you could play:

-   F or F# - a minor 2nd or major 2nd interval above E, which would create a dissonant clash
-   A - a minor 6th interval above E, which is also dissonant and outside the key of E major

Playing notes a semitone or whole tone away from the notes in the key of E will create tension and dissonance. The further away from the key you get, the more discordant the effect.