Since mistake done, let try to fix it
Some bros recommend :
1. Sell one of them
2. Try rescape (but doesn't work for my previous nano, I think tank too small even how we scape they still not happy)
3. Mirror methods (sometime works I observed tangs team up and aggainst mirror )
4. QT them with partition and dimmer, release after few weeks. ( to avoid additional stress induce in your main tank )
5. Partition your tank combo with mirror, release them after few months.. (Most likely works.. cause they already used to your tank condition.. and knowing each other strength. they will develope their own pecking system.. Weaker give way...)
some reference:
http://www.sgreefclub.com/forum/index.php?showtopic=88493&st=0&p=909029&hl=partition&fromsearch=1&#entry909029
Normally, for Yellow tang and Purple Tang. I suggested get slight smaller Purple tang than yellow one... Cause Purple tang known to be more aggresive and stronger....
Above just share my own opinion and learning from others guru.....
Cheers and Happy Reefing...