Momentum - related question

I have been trying to solve this problem for quite a while now, I even asked one of my teachers and they found it hard and could not solve it.
So,

A stationary unstable nucleus of mass M emits an alpha particle of mass m with kinetic energy E .

What is the speed of recoil of the daughter nucleus ?

The answer is
A ) √2mE / (M-m)

I've attached a photo of the question so you also see the diagram, maybe it helps.
( https://imgur.com/8UbT5Jg )
But I do not know how to get to it. Can anyone explain it step by step please? Thank you !

I got this far, but I don’t know how they get the m on the top of the fraction, maybe you could work it out from here?

Alpha particle has mass m and kinetic energy E, so if it's speed is u, then we have $E=\frac{1}{2}mu^2$

And we can rearrange to get $u=\sqrt{\frac{2E}{m}}$.....(1)

Mass of daughter nucleus is M-m, and let it's speed be v.

Then by conservation of momentum.

$mu=(M-m)v$

Make v the subject and substitute for u from (1)