My advice would be to ask the first company for a little more time and to try to push the second company to move up the interview date. I don't know your situation but some people, if they are taking a vacation or have personal business, ask if they can delay a decision until after they return from their trip. I would just try to buy some time. This is the part of the job search that gets interesting. Risk-takers find it invigorating.
Most people find it mind boggling.
There is no way to completely predict the outcome. You must understand the risks you are taking when choosing how to proceed. Yes, that's right. Even the stuff they claim they cannot bend on. Always play out your probable responses and worst case scenarios.