Captain reported trailing edge flap failure EICAS message on approach. The flight crew discontinued the approach; ran the check list and QRH procedures; and flew a no flap landing at destination airport.

Narrative

This leg was the last leg of a four-day trip for myself and First Officer NAME. We departed ZZZ1 and continued to ZZZ without incident until we encountered a Flap Failure during the approach phase into ZZZ. We were on the ZZZZZ arrival; Runway XX transition and was just beginning the approach phase when First Officer NAME; as the Pilot Flying; requested 'flaps 9'. I selected flaps 9; and almost immediately 'FLAP FAIL' was indicated in the EICAS. I announced the EICAS indication to First Officer NAME; and he confirmed. My first reaction was to calculate our extra fuel on board; I conducted a quick mental math calculation concluding that we had at least 10 extra minutes of fuel to run the QRH; take care of all necessary duties; and prepare for landing. I then notified ATC that we had a flap issue and that we would need extra time prior to prepare for landing. I also notified them that we had an extra 10 minutes of fuel so that they could plan accordingly. After ATC gave us delay vectors; First Officer NAME and I discussed fuel available and next steps. I then turned to page X-X in the QRH for the FLAP FAIL procedure. First Officer NAME and I conducted the FLAP FAIL procedure in the QRH. We also notified Dispatch via ACARS; communicated numerous times with the Flight Attendant; including providing an [briefing]; and made an announcement to the passengers notifying them of the situation. First Officer NAME and I discussed if we would request priority handling or not. We discussed the fact that we would be landing at high speed with a risk of exiting the runway and the risk of fire due to excessive brake heat. We agreed the best course of action was to request priority handling; and we did so. After we had ample time to double check that the QRH items were completed--particularly that we calculated an accurate ref speed and also calculated minimum runway length required--we notified ATC that we were prepared to execute the approach and landing. We transferred controls; and I executed the no flaps landing without incident. After arriving at the gate; we debriefed; I wrote up the flap fail and discussed the incident with Dispatch and the on duty Flight Manager.Provide more contingency fuel.