Translation:Our school needs a teacher of Japanese.
Well, "Our school needs a teacher of Japanese" means specifically that the person will be teaching the Japanese language. "Our school needs a Japanese teacher" can mean that, but it can also mean that the school is trying to diversify its staff and is trying to hire a person of Japanese descent.
From my understanding (not a native speaker) японского is the genitive of the noun японский (Japanese, the language). So my guess would be, that this sentence can only mean that he is teaching Japanese.
A teacher of Japanese descent (that may teach mathemetics or something else unrelated to the Japanese language) should be японский учитель. Нашей школе нужен японский учитель.