Why conservation of energy here vs momentum?

1. The problem statement, all variables and given/known data

A billiard ball moving at 2.58 m/s collides elastically with an identical ball initially at rest. After the collision the speed of one ball is 1.36 m/s. What is the speed of the other?

2. Relevant equations

K1+K2=K1‘+K2

or

P1+P2=P1‘+P2

3. The attempt at a solution

I get the correct answer using conservation of energy and the wrong answer using conservation of momentum. My understanding is that conservation of momentum problems work for both elastic and inelastic problems whereas conservation of energy work for elastic problems only (unless energy lost is known).

In this case the masses cancel out so both methods (momentum/energy) actually look the same when solved symbolically other than the energy equation yields squared velocities and the momentum equation does not.

How do I know to use conservation of energy here instead of conservation of momentum? Shouldn’t momentum also be conserved?

Thank you!

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