In this question, @whuber writes in his reply that

If you were willing to assume something about that common distribution (such as it is some Normal distribution--but without knowing or assuming anything about its parameters) then tests exist--even when only a single pair (x,y) is observed (which most people find counterintuitive). Without some kind of assumption, though, your task is hopeless, because you have no information about how much of a difference can be considered "negligible."

I would be interested how such test is carried out (let's assume a normal distribution).