Diane ,E dorian is not what you described,It has two sharps f#c#,unlike E major[which has 4 sharps] it does not have g# or d#.what you describe sounds more like D dorian,starting on the piano at d and playing all the white noteto the next d.
What defines dorian mode is the major scale, altered by flattening the third and the seventh.takeE major[4#]flatten the third g#and the seventh d#,and youhave it.Dick Miles