Second: talk to your manager. Don't send an e-mail. That would just turn in a long, and possibly bitter, battle of 're:re:re:re:' or be interpreted as a C.Y.A. fig leaf. Make sure you start by understanding where that timebox is coming from and how 'un-elastic' really is. Then proceed to explain that for your team it's hard to commit to a timeline when the - currently unknown - fix to the bug could be a line of code or rewriting a whole component of the software. Reach an understanding that - of course - your team will try an deliver in the gives timebox if at all possible, but that you will keep him informed of any findings that may indicate that it will take longer.
Third: proceed working on the analysis and fix keeping them in the loop; make the messaging short, meaningful and to the point. "We found the issue: X", "We're designing a fix: Y", "Current estimate for the fix is Y". Make sure that the communication is timely. One thing is to say at 10AM: "We think it's going to take two days", and another is to say the same thing at 5PM.
Ideally this should come from the Dev team lead - which is what I do for a living. We are there to take the fire.
If you get pushback, no answers and management doesn't respond well to this pattern - well, you want that career destroyed and to move to some other place.