B777 Captain reported an engine failure during takeoff roll. Flight crew rejected takeoff and returned to the gate

Narrative

We taxied on the runway XX for takeoff for intersection; everything was normal we were cleared for takeoff the left engine was slow coming up; I held the brakes and waited for the engines to be stabilized. As I advanced the throttles I called for check thrust; the FO said thrust checked at that time the aircraft veered right and I heard 2 bangs and an Engine fail EICAS at about 40-50 KTS with a shaking to the aircraft. After applying the brakes and centering the plane on the runway we came to at stop; my report made an announcement to remain seated on the PA. I looked down at the engine indications and everything was normal with both engines running. My FO told the tower we had rejected on runway XX and told them we would like to taxi off the runway; they asked if we needed any assistance and with everything being normal she said not at this time. We ran the checklist; called the flight attendants to see if they had anything in the cabin they said they heard the loud bangs but everything was okay back there. We taxied off Taxiway 1 and stopped on Taxiway 2 as instructed by tower we took a deep breath and accessed the situation; my FO stayed with tower my report talked to the FAs and I called Dispatch with a phone patch to Maintenance Control; they confirmed we had an engine surge and engine fail. They recommended going back to a gate we coordinated with operations and taxied to handstand; the right engine would start getting to approach over temperature with any input so I taxied with 1 engine. We all commented that it seemed like a perfect solution to a problem. Mechanics came on board looked at the bleed valves and told us that they needed to do more work and it could be days to repair the problem. My report and myself made several announcements keeping the passengers and flight attendants informed.