Dear Brother(1991)

Onii-sama e...

Before leaving her cram school, Nanako Misonō asks one of the teachers if they can become pen-pals. The teacher, Takehiko Henmi, is reluctant at first, but eventually accepts the offer. The story is narrated through the letters sent from Nanako as she enters Seiran, a renowned private high school for girls only. There she encounters many difficulties as an ordinary middle-class girl invited to the prestigious Sorority, the most traditional and sophisticated club on campus..

(Source: AnimeNewsNetwork)