From watching the first episode ...
So far the story is about Yukitaka who is considered a middle-school baseball champion (but apparently he spent most of the last season on the bench) who ends up having an alien living with him.
I'll spoil the name since it's easier than saying 'the alien' all the time :P
'Prince' seems to have lost his memory when he crash landed near where Yukitaka ends up living.
Prince went to Yukitaka's place before Yukitaka got to move in and that's how they meet - the first time Yukitaka enters his new place for while he's in high school.
Also next door is Miho who moves in about the same time and also starts in first year at the same high school.
Her father happens to be one of the people researching Prince's alien ship that crash landed (before Yukitaka made it explode)
Story is pretty droll so far but no doubt I'll add it as something to watch each week after I've watched all the other shows I'm getting :)
Ep 1 is the same name as the first manga chapter.
Ep 2 is also the same name as the 2nd manga chapter.
16 Chapters of Level E where done back in 1995-1997 so at a guess the anime may be the whole 16 chapters in 12 or 13 episodes.
The mangaka is Yoshihiro Togashi who also does the ongoing Hunter x Hunter (1998-current)
He is also married to Naoko Takeuchi, the author of Sailor Moon.