In response to your question: DO NOT connect the two conductors together.
Two things you need to pay attention to. First make sure that the conductors have not been painted over. In many cases the conductors appear to be the same color, but by scratching and scrapping the true color will become apparent.
Second, because general house wiring is in NM and it's usually a black and white conductor, it is not against the NEC to have white conductors as current carrying conductors. It should be marked as a non-neutral. For example it is wrapped with black tape which may have fallen off or just not done. The only problem I see is if it has two white conductors, it generally indicates that that receptacle is on a switch or the branch circuit is tapped somewhere.
If you need to find which white wire is hot. You can do this by using a multi-meter and find which conductor has nominal voltage between that conductor and the ground (the bare or green wire). You might be able to use a non-contact voltage detector, but they can be a little unreliable. If you do find the hot conductor then you can mark it, then reconnect it and it wouldn't be a bad idea to find the tap and see what the "tinker" was up to.
Hope this helps and good luck.