The problem then states: estimate the minimum wavelength of the gamma ray photon.
The answer to this question is: 0.25 x 10^-11 - (binding energy of oxygen - the binding energy of F which is 0.04 x 10^-11). Then you use the hc/E = wavelength which I understand.
What I don't understand is why you would minus the kinetic energy from the energy released during nuclear fusion? Where does the kinetic energy of the proton go; does it turn into mass of fluorine? I just don't understand; I would have added the oxygen binding energy and kinetic energy of the proton together and then subtracted that value from the binding energy of fluorine-18.