I'm not following that solution all that well.
With R being the distance in AU from Sun, it's easy to get the force per unit area from the Sun using the equation:
9e-6 /R^2, which gives N/m^2
From here.
[This assumes a perfect reflection efficiency]
Knowing the force, you can easily get the acceleration for a given mass (a = F/m).
But this force is reduced in accord with inverse square law.
Also, at more relativisitc speeds, the photons have less energy due to redshift, also affecting accelaration.
[I tried p = 2E/c, where p is momentum and E is energy (J). But that gives Joules/m, not Joules-sec as needed for force. So I'm forgeting something, obviously.]
Another solution found is using:
F = 2*L*a* cos() / (4*pi*r^2 * c), where r is the radius of the sail; L is the luminosity of the Sun; a is the sail area. Cos() is 1 when the sail is perpendicular to light flux.