plotting - Roots of a characteristic equation. Can Mathematica solve it?

I have been using Mathematica for a few years, but with basic things. Now I need to find the first 10 roots of the following equation:

Cos[y] - 2 E^(-y)/(1 + E^(-2 y)) == 0

I have been trying to use the commands Solve, SolveAlways and FindRoot. But the only one that worked is the last one, but it needs a value near the root. Could you help me?