Absolute Duo

The story begins with Blaze — a weapon that is the manifestation of a human's soul. Tooru Kokonoe happens to be qualified for this, but for some reason his Blaze is not a weapon, but a shield. Moreover, he enrolled in a school that teaches combat skills, and thanks to the school's Duo partner system, he ends up living with a beautiful silver-haired girl.

(Source: Anime News Network)