Umeda and Akiha (and Ryouichi)

So, especially given the happenings of a recent thread, some of y'all must be wondering what the flaming heck is up with Umeda and Akiha, anyway. Do they like each other? Dislike each other? One-sided love? And if it's the last, why has Umeda invited Akiha back to his office?

( WARNING. The following has spoilers for the manga up to the final, extended chapter. )