Actually, an E dorian piece will end on E because that's the key tone. However, it will have the same key signature as D major - two sharps.

Without going into a lot of theory, here's a quick way to spot modes:

    Ionian = major, so key signature and key tone will match. C = no sharps or flats, G = one sharp (F#), D = two sharps (F#, C#) etc.

    Aeolian = minor, key signature and key tone will match normal expectations, i.e. the key signature will be the same as it's relative major. Am = no sharps or flats, Em = one sharp (F#), Bm = two sharps (F#, C#), etc.

    Mixolidian = sounds major, but with a flatted seventh, so it looks like it's missing a sharp. C mix = one flat (Bb), G mix = no sharps or flats (F is natural), D mix = one sharp (F#, C is natural), etc.

    Dorian = sounds minory, but with a sharped sixth, so it looks like it has one sharp too many. A dor = one sharp (F#), E dor = two sharps (F#, C#), B dor (F#, C#, G#) etc.

Some publishers write Mix & Dorian tunes as if they were major and minor and use accidentals for the extra flats and sharps (ie a D mix tune would have the key signature of D major, but all the C's would have a natural sign), others use the key signature that fits the mode, but the key tone looks out of whack for the signature (ie a D mix tune would have the key signature of G major - one sharp - but the key tone would be D rather than the expected G).

There's no consistency on this, and only rarely do publishers acknowledge that the tune is modal, even though lots of folk music is modal. I've had fun going through my books and figuring out what the mode really is - and there are lots of tunes, especially Irish ones that shift mode without changing key tone.