Answer
$K = \frac{p^2}{2m}$
Work Step by Step
Note that if $K \lt \lt E_0$, then the expression $K^2+2KE_0 \approx 2KE_0$
We can find an expression for $K$:
$(pc)^2 = K^2+2KE_0$
$(pc)^2 \approx 2KE_0$
$K = \frac{(pc)^2}{2E_0}$
$K = \frac{p^2c^2}{2mc^2}$
$K = \frac{p^2}{2m}$
