B757 Captain reported a flap asymmetry occurred during approach when flaps were extended. The flight crew completed a go-around and returned to land.

Narrative

This was the 2nd Leg of a right seat checkout for a new Line Check Airman (LCA). The LCA (s) was the Captain and pilot monitoring (PM). LCA Candidate was in the right seat and pilot flying (PF). Executing a Flaps 25 visual approach; backed up by the LOC to Runway XXR. Level at 2000 at 170 kts.; Flaps are at 5. VNAV selected; VNAV Path displayed PF called for 'Flaps 20; LDG Gear down' PM placed Landing Gear down; and Flap handle to 20. PM Armed the Speed brake and looked up and had the TE FLAP ASYM EICAS MSG was displayed. PM made sure handle was in the proper detent (it was). Flap indicators were split; with a single needle on both sides of the Flaps 15 Indication. PM announced that we were going to have to do a go around. PM informed Tower that we were going to go around due to a flap issue. Tower instructed us to climb to 3000 and right hand turn to 030. We executed a go around and complied with instructions. PM announced the fuel was at 7.9 on the go around. Once level we opened up the QRH and performed the TE Flap Asymmetry Checklist. We had the same shared mental model on we wanted as far as [requesting priority handling] and requesting Runway XXC due to a higher approach speed. We also [requested priority handling]. It was determined that the Flaps were between 5 and 20 so the REF speed of Flaps 30 + 30 KTS. We came up with a VREF of 150 based on our weight. PM completed the checklist and then performed the In-Range and Approach Deferred Items checklist. PM discussed that the sight picture would be a little bit flatter and to use Max Reverse Auto brakes 2. PF flew a good approach to a smooth touchdown. PF used Max reverse. Aircraft exited at XX to X. PM told Tower that we would not need any further assistance. We taxied to the gate with no further issues. We did have brake temp sensors on this jet and the temps never got above 2. As we approached spot 10 the fuel was 6.3.Cause - TE Flap Asymmetry. TE Flaps split at flaps 15.