Can a Super Flare Defeat a Black Hole?

In Superman #38, Superman in his battle with Ulysses unleashes the super flare, that releases all the energy stored in his cells and makes him human for 24 hours.

From IGN:

In the pages of today’s Superman #38, Superman’s discovered he has a new “super flare” power where he expels all of the energy in his cells to create a bright, powerful blast capable of incinerating everything within a quarter mile. The downside — aside from the mass destruction — is that using the super flare ability depletes his cells, essentially making Superman human for 24 hours.

– ‘Superman’s New Super Flare Power and Costume Revealed’, IGN

During his fight with Ulysses, a meta-human who can absorb energy, Superman blasted Ulysses with heat vision that Ulysses absorbed which resulted in Superman unleashing his Super Flare, as he started to glow. (Superman’s New Super Flare Power and Costume Revealed)

The fight resulted in the destruction of Superman’s armor costume in the New 52 multiverse which was created as a Kryptonian nano-tech armor that would cover his body, and the creation of a new costume.

At the end of the comic book, Superman reveals his secret identity to Jimmy Olsen: “I’m Superman Jim.”

Can a Super Flare Defeat a Black Hole?

In JLA Vol 1 #77 (2003), Superman holds ” a black hole no bigger than a speck of dust that is contained by a magnetic field”. The black hole is named Mnemon, it steals memories and causes the Justice League to fight among itself. Superman contains the black hole and with the help of GREEN LANTERN John Stewart flies it “to a desolate stretch of space and hurl[s] it away.” (JLA Vol 1 77)