Solving a transcendental equation with some parameters

I’m trying to solve a transcendental equation:

NSolve[
  a (1/2 
    (a Sqrt[1 - a^4/b^4 - a^2/b^2] + 
      (b^2 ArcSin[(a Sqrt[a^2 + b^2])/b^2])/Sqrt[a^2 + b^2]) + 
    1/2 (Y Sqrt[1 - (a^2 Y^2)/b^4 - Y^2/b^2] + 
      (b^2 ArcSin[(Sqrt[a^2 + b^2] Y)/b^2])/Sqrt[a^2 + b^2])) == 
  mg/(2 B), Y]

But it didn’t work. I got this message:

NSolve::nsmet: This system cannot be solved with the methods available to NSolve.

Any suggestion for me to get a numerical solution or even an approximation?