  Using a nonlinear electrodynamics coupled to teleparallel theory of gravity,
three regular charged spherically symmetric solutions are obtained. The
nonlinear theory reduces to the Maxwell one in the weak limit and the solutions
correspond to charged spacetimes. The third solution contains an arbitrary
function from which we can generate the other two solutions. The metric
associated with these spacetimes is the same, i.e., a regular charged static
spherically symmetric black hole. In calculating the energy content of the
third solution using the gravitational energy-momentum given by M{\o}ller,
within the framework of the teleparallel geometry, we find that the resulting
form depends on the arbitrary function. Using the regularized expression of the
gravitational energy-momentum we get the value of energy.
