  We give two classes of spherically symmetric exact solutions of the couple
gravitational and electromagnetic fields with charged source in the tetrad
theory of gravitation. The first solution depends on an arbitrary function
$H({R},t)$. The second solution depends on a constant parameter $\eta$. These
solutions reproduce the same metric, i.e., the Reissner--Nordstr$\ddot{o}$m
metric. If the arbitrary function which characterizes the first solution and
the arbitrary constant of the second solution are set to be zero, then the two
exact solutions will coincide with each other. We then calculate the energy
content associated with these analytic solutions using the superpotential
method. In particular, we examine whether these solutions meet the condition
which M{\o}ller required for a consistent energy-momentum complex: Namely, we
check whether the total four-momentum of an isolated system behaves as a
four-vector under Lorentz transformations. It is then found that the arbitrary
function should decrease faster than $1/\sqrt{R}$ for $R\to \infty$. It is also
shown that the second exact solution meets the M{\o}ller's condition.
