Solve large equation with parameters?

Questions
,
1

I have a very large expression:

j - Sqrt[q^2 + qp^2 - 
   2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 + 
     1/2 (16 m5^2 + ma^2 + mp^2 - 
        Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 
         4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0

where

\[Theta] = Pi/6; ma = 980; mp = 139;
 j = \[Sqrt](q^2 + 
    1/2 (16 m5^2 + ma^2 + mp^2 + 
       Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 
        4 (ma^2 mp^2 - 16 m5^2 q^2)]))

And qp is real and positive.
I want to find qp as function q>0 and m5>0 (if it is imposible then function only q>0 and m5=constant=100>0).
I atemted to solve this the next way:

Solve[ j - Sqrt[
     q^2 + qp^2 - 
      2 q qp Cos[\[Theta]]] - \[Sqrt](qp^2 + 
        1/2 (16 m5^2 + ma^2 + mp^2 - 
           Sqrt[(-(16 m5^2) - ma^2 - mp^2)^2 - 
            4 (ma^2 mp^2 - 16 m5^2 qp^2)])) == 0 && qp > 0 , qp, 
  Reals];

Mathematica hangs after two hour calculation. Where I am wrong?
After calculation I want to plot function form: z=q^2+m5^2 (in reality this is more complicated)

x-post on MSE:
link

2

Please add links to/from x-post on MSE.