AN EMB145 CREW EXPERIENCED A LARGE BOOM FOLLOWED BY A #2 ENG FAILURE. THEY DECLARED AN EMER AND DIVERTED TO A NEARBY ARPT.

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WE WERE CLBING THROUGH FL260 WHEN WE HEARD A LOUD BOOM FROM R SIDE OF ACFT. LOOKING AT ENG INSTS ON #2 AND NOTICED THAT ITT WENT IN THE RED. WE IMMEDIATELY PULLED THE THRUST LEVER TO IDLE. E2 OUT MESSAGE APPEARED ON EICAS. DECLARED EMER WITH ATC AND ASKED FOR A TURN TO ZZZ. FOLLOWING COMPANY PROCS WE PROCEEDED WITH E2 OUT ABNORMAL CHKLIST; THEN PRECAUTIONARY ENG SHUTDOWN CHKLIST. DISPATCH WAS CONTACTED NEXT WHO ADVISED THAT THEY WISHED FOR US TO DIVERT TO ZZZ1. WE THEN ADVISED ATC WE WISHED TO PROCEED TO ZZZ1. ATC THEN GAVE US DIRECT TO ZZZ1. TOLD FLT ATTENDANT WE HAD AN ENG OUT AND TO START HIS STEPS. CHKED ENG INSTS AND OIL QUANTITY; WHICH WAS 10 QUARTS. THEN PROCEEDED WITH ENG AIR START CHKLIST WITH APU ASSISTED START. WE WERE THINKING THAT IF WE GOT THE ENG STARTED IT WOULD BE BETTER TO HAVE THAT EXTRA THRUST THAN NONE AT ALL. DURING ENG START; SAW THERE WAS NO ITT RISE THEN WE SHUT IT DOWN. ATC GAVE US RADAR VECTORS TO RWY 6 ILS AT ZZZ1. THEN ONE ENG INOP APCH AND LNDG WITH ONE ENG INOP GAR CHKLIST COMPLETED. THEN NORMAL DSCNT; APCH AND LNDG; AND LNDG CHKLIST WERE COMPLETED. CLRED FOR ILS RWY 6 AND CLRED TO LAND RWY 6. ATC ASKED IF WE NEEDED EMER EQUIP. OUR RESPONSE WAS YES THINKING HAVING THEM THERE IS BETTER THAN NOT HAVING THEM AT ALL. WE LANDED SAFELY AND ROLLED TO THE END OF RWY WHERE WE EXITED SAFELY. RAN AFTER LNDG CHKLIST AND THERE WAS NO NEED FOR EVAC OR EMER VEHICLE ASSISTANCE; AND TOLD GND EMER EQUIP WERE NO LONGER NEEDED. TAXIED TO GATE WHERE WE SHUT THE PLANE DOWN AND DEPLANED NORMALLY.