Your differential equation is easily solved, and it means that e(w)=c*w for some constant c. You are looking for solutions of the very complicated nonlinear equation toBeZero ==0 that are straight lines through the origin. Are you sure that there is such a straight line? I tried for a while, and could not find it.

From the following plot

myTwoEQs = Block[{n = 1, W = 60, i = 1/10, b = 6/10, a = 1/2},
      {#, Dt[#, w]} &@myEQ] /.
      {e -> e[w]} /. {e'[w] -> e[w]/w} /. {e[w] -> e};
ContourPlot[myTwoEQs, {e, 0, 1}, {w, 0, 2}, PlotPoints -> 200, 
 ContourStyle -> {Directive[Blue, Thickness[.01], Opacity[.2]], 
   Directive[Darker@Red, Thin]}]

it would seem that the system of the two equations has infinitely many solutions, along a whole line (near the left side of the plot). If this is correct, then the command

icEQ = myTwoEQs /. Equal -> Subtract;
icSOL = NSolve[icEQ == 0 && 0 < e < 1 && 0 < w < 2, {e, w}]

cannot possibly work. I would rather give a fixed value for w, for example w==1.

A closer look suggests that the situation is complicated:

Plot[Evaluate[
  myTwoEQs[[1]] /. Equal -> Subtract /. w -> 1], {e, .0191, .0192}, 
 PlotRange -> 10 {-1, 1}]