There is no way in a transaction to determine what is "my output" and "your output". That is what makes coin join work, but also brings up the problem originally posed.
Your output is the one that you have the key to spend. What's hard about that? There may be no way for anyone *else* to tell whose output is whose, but you are the guy who created that key pair, you still have the private key, and you know damn well whether a given output has the corresponding public key. In a coinjoin everyone can identify their own outputs. But they can't distinguish anyone else's, and no third-party observer can distinguish them at all.
We might be talking about different outputs. The original question was not about the TxOut that is an input to the CoinJoin transaction, but instead the outputs of the CoinJoin Transaction itself. AFAIK, there is no way for me to get Wikileak's private key.