Some good books on Numerical methods are:

Numerical Recipes in Fortran 77 by Press, Teukolsky et al. (Good on algorithms and their implementation)

A first course in the numerical analysis of differential equations by Iserles. (A good book for the theoretical understanding)

Numerical solution of partial differential equations by Smith (very good on finite difference methods).

The simplest BE method is ofcourse a 1st order scheme which for your problem will be:

,

.

As you can see the only difference between the Backwards and Forwards Euler methods is where the derivative function is evaluated. In the forward case it is evaluated at the step whilst for the backwards case it is at the step. Hence for the backwards case it is an implicit equation that needs to be solved that usually requires the inversion of a matrix.