Can this equation be solved for F?

F/3500 = [85+(1750/F)^2)^-.5] + [74+(1750/F)^2)^-.5]

Just to be clear, this equation is read:

(F divided by 3500) equals (85 plus (1750 divided by F) squared) all to the negative one half plus (74 plus (1750 divided by F) squared) all to the negative one half.

Sorry I don't know latex.

...And for your own sake do not try to solve this equation. I am 99% sure it cannot be done unless it involves a computer program and/or imaginary numbers.

I am just hoping someone can tell me if it can or cannot be solved and why.