Piano Forum

Yes the same note is in both parts
You could play this in an organ but with the piano one note has to go

Harmonically it makes more sense for the hands movement to get rid of the left hand E and just play the right hand E ... that's because it would be harder to maintain the A - F - G - E legato by lifting the right hand and playing the E with the left hand so that it sounds legato to the right hand.

I've been playing these inventions (I've done 1 through 4 and I am working on No. 5 now). My piano teacher recommends (if possible) to try to position a finger from both hands in the area of the key like both are playing it. This helps in making sure that you don't play the previous note longer for the hand that is not playing the simultaneous note. I can see how that can happen, especially in polyphonic music where you are concentrating on which notes to play next and not so much on notes that just flew by  , so you could leave the hand that is sitting out the note a bit too long on the key. In any case - it worked for me!