Assuming the headers are in H1:U1, how about:
=IF((COUNTIF(H2:U2,">="&E2)-COUNTIF(H2:U2,">="&F2))=0,"",
INDEX(H1:U1,MATCH(1,(H2:U2>=E2)*(H2:U2<=F2),0)))
This is an array formula. Hit ctrl-shift-enter instead of enter. If you do it
correctly, excel will wrap curly brackets {} around your formula. (don't type
them yourself.)
ps. I changed your " " to "", too.
I also included the end dates with >= and <=. Did you want them included?
The formula determines if any of the dates in the range of H2:U2 are between
the dates in cells E2 and F2, and if not the cell remains blank. If there is
a date in that range that is between the dates in E2 and F2 the cell is given
the word Due. Rather than the word Due, I want an equation that will find
the date and then return to the cell the column header of that cell.