Is there a cure for a type of hearing loss called tinnitus?

No. Basically, hearing loss is irreversible. There are cochlear implants, but those aren't a reversal of hearing loss, just an aid to improve hearing. Tinnitus is actually common for many people. Most people get it, but extreme tinnitus is a constant problem and results in hearing loss. In those cases, the damage is generally not reversable. However, ringing in the ears goes away in most people if it isn't serious.