Initially, E is equal to initial kinetic energy when the ball is released.

At height h, PE=KE, TE=PE+KE, then TE=PE+PE=2PE.

Then when velocity is doubled, KE'=4E. It is the total energy initially when PE=0.

At height h, TE=4E=8PE=KE at height h+PE

KE at height at h = 8PE-PE = 7PE.