$12\mathrm{.}28.$ Another perpendicular photon $*$

A mass $m$ moving at speed $4\frac{c}{5}$ collides with another mass $m$ at rest. The collision produces a photon with energy $E$ traveling perpendicular to the original direction, and a mass $M$ traveling in another direction, as shown in Fig. $12\mathrm{.}25.$ In terms of $E$ and $m,$ what is $M?$ What is the largest value of $E($in terms of $m)$ for which this setup is possible?

Fig. $12\mathrm{.}25$