How fast must a neutron be travelling relative to a detector in order to have a measured kinetic energy that is equal to its rest energy?

I know
Ek = mc^2 - m0c^2

But if Ek = m0c^2, wouldn't the two terms cancel out from this equation? I am having trouble going about with it mathematically, and could use a few pointers if you guys don't mind helping out.

Where m0 is the rest mass.
m is the relativistic mass

Question

How fast must a neutron be travelling relative to a detector in order to have a measured kinetic energy that is equal to its rest energy?

I know
Ek = mc^2 - m0c^2

But if Ek = m0c^2, wouldn't the two terms cancel out from this equation? I am having trouble going about with it mathematically, and could use a few pointers if you guys don't mind helping out.

Where m0 is the rest mass.
m is the relativistic mass