When you write songs, does the melody come first, then the chord changes?
The truthful, but uninformative, answer is it varies /there are no rules no rules , yaddah yaddah...
But I'll second tZer's point: Ultimately, a good melody is the goal. When I start with a melody, it generally is stronger and more ear pleasing than if I start with a groove or set of chords and try to fit a melody into it.
I've got NO idea how to come up with a chordal melody...
Harmonizing a melody requires some basic theory...and the farther outside the major scale your melody is, the more theory you'll probably have to draw on.
Simplify your chord choices.
First: What key is the melody in?
You say it's E, so I'll assume you know what your talking about and it's a melody in E major.
the
diatonic chords of E major are : E, F#min, G#min, A, B7, C#min, and D#dim.
I helps if you know
how to build chords from scales.
if your melody really is E major, then you can harmonize with these 7 chords alone ( yes there are more possibilities, but KISS at first)
With this ammo, you can just grab the nearest guitar or piano and start singing and experimenting to see what fits.
Keep in mind that the chord should almost always contain the melody note, either as its root, 3rd, 5th, or 7th (higher chord tones are also possible, but KISS)
Some times choosing between 7 chords is too much, and you can narrow it down to the absolute minimum: I, IV, and V (E, A and B7 in this case.)
With only three choices you can quickly get close to what will work.
then you can substitute related chords to see which might fit better:
I is related to iii
IV to ii and vi
V to vii(dim)
If your melody is minor or some other mode, this approach will have to be mapped onto that mode. If it changes keys or is even more complicated, well, time to it the books.