Rule number one : Stay Calm!!
then get a metal chisel and hammer, cut the head off that 10mm bolt, remove what has to be removed, then see if you can grab the end with a good pair of Visegrips to remove the remaining bolt. IF Visegrips don't work, then I suggest you drill it out and re-tapp the hole. When you're ready to put a new 'bolt' back in. Try not to cross thread this time.