It seems that Y and E are both very clear on what they want. Y wants his home and marriage back. E wants to live in Y's home and sleep with his wife.
I have my doubts that any amount of talking is going to change this.
I think we've come to a point where we believe, as a society, that we can have it all, that we never need to make hard choices or give anything up, if we just really, really, really want it, if we just find the right words, and communicate well enough, and use the right technique to get to the bottom of things.
No. Y wants a monogamous marriage and the two of you in your own home. E wants to remain there and remain in a relationship with you. Maybe enough talking will convince Y to continue to accept the situation, but I can't foresee him ever being happy with it, given what you've said.