The Morose Mononokean(2013)

Fukigen na Mononokean

Ashiya has spent the first seven days of high school stuck in the infirmary because of a youkai attaching itself to him. He ends up asking the owner of a small tea room called the "Mononokean" for help. This is a tale involving the very morose owner of Mononokean guiding the youkai that happened to wander into this world go to the next world.

(Source: Crunchyroll)

Note: Includes 1 extra chapter.