You cannot start from the expression given, because that is the answer which you are being asked to find.
You should use the usual procedure as in classical mechanics - ie write equations for the conservation of total energy and linear momentum. The fact that the collision is described as elastic means that the rest mass of each particle is the same after the collision as it was before.
Label the particles $1$ and $2$. Then :
$E_2=m$ and $P_2=0$, and $E$ and $P$ are related by $E^2=P^2+M^2$.
Rearrange these 2 equations to get $E_2'$ and $P_2'$ then substitute into $E_2'^2=P_2'^2+m^2$. The final equation contains $E_1, E_1'$; rearrange to find $E_1'$.
The calculation is quite involved, as you can see from the complexity of the result for $E_1'$ the final energy for the incoming particle $1$.
After a lot of algebra I get