On uniquely weakly clean rings

Let $ R $ be an associative ring with identity. An element $ ain R $ is said to be weakly clean if $ a=u+e $ or $ a=u-e $ for some unit $ u $ and idempotent $ e $ in $ R $. The ring $ R $ is said to be weakly clean if all of its elements are weakly clean, if this representation is unique for every element, we call the ring uniquely weakly clean.