There are only two ways Braun can get out of this. He either needs to scientifically prove that the test was a false positive (which might be hard since a follow-up test showed synthetic testosterone), he was re-tested a few weeks later which came back negative. That second test is not necessarily relevant, but he's arguing that the difference between the extremely high first result and the extremely low second result was so big, that it proves a false positive. I don't know the science behind this, I assume the folks at the lab will explain what happened and why Braun's argument is or is not valid.
If that doesn't work, Braun would have to prove that food or supplements he was taken was tampered with by someone else without his knowledge. Baseball has a strict liability policy, meaning that not knowing something you were taking had a bad substance is no excuse, you have to show you were not carelessly consuming stuff without knowing what is in it. The only way to successfully appeal, aside from attacking the test result, is to basically prove that someone spiked your food. Good luck with that argument.
how many emo kids does it take to change a lightbulb?
none they just sit in the dark and cry