How can I plot $\kappa(\epsilon_{dd},\lambda)$  this transcendental equation?
$$3\kappa \epsilon_{dd}\left[\left(\frac{\lambda^2}{2}+1\right)\frac{f_s(\kappa)}{1-\kappa^2}-1\right]+(\epsilon_{dd}-1)(\kappa^2-\lambda^2)=0 $$
where $\lambda=1,2,3,4$ and 
$$f_s(\kappa)=\frac{1+2\kappa^2}{1-\kappa^2}-\frac{3\kappa^2 artanh \sqrt{1-\kappa^2} }{(1-\kappa^2)^{3/2}}. $$

My original problem is not that, but it's similar. If you help me with this, maybe I can solve mine.

Here are the codes of equations:

    fs[kappa_] := (1 +3 kappa^2)/(1 - kappa^2) - (3 kappa^2 ArcTanh[
      Sqrt[1 - kappa^2]])/(1 - kappa^2)^(3/2)

    3 kappa edd (((lambda^2/2) + 1) fs[kappa]/(1 - kappa^2) - 
     1) + (edd - 1) (kappa^2 - lambda^2) == 0

[![Original plotting][1]][1]


  [1]: https://i.sstatic.net/jsqWw.jpg