If you think about the mathematical calculation of such a problem, it looks quite complicated. It will take several days of work and several books on theoretical mechanics.
But you can do it easier. Make a 3d model of the gear you need with the help of specialized programs like GearTeq or GearTrax. Then just increase the distance between the gears in the model and measure the backlash.
Sorry, necropost but ... in truth, it is extremely simple. If you are using standard proportions, one of the numbers is the tooth thickness. Just reduce it by the amount of backlash you want. Can take it off both gears or either one, depending on the situation.
If it's a practical matter in the manufacture, if you are measuring using the span method, same thing. Just reduce the theoretical measurement by the amount of backlash you want.
If it's measuring over wires, depends on the pressure angle. For 14.5* teeth, the tooth thickness is about 1.4 times the depth, so to get .002" backlash on one gear, drop the wire measurement in by .003" (it's okay to round off, backlash isn't that picky.) If they are 20*, it's pretty much 1:1 so drop the mow by the amount of lash you want.