  A non-diagonal spherically symmetric tetrad field, involving four unknown
functions of radial coordinate $r$, is applied to the equations of motion of
f(T) gravity theory. A special exact vacuum solution with one constant of
integration is obtained. The scalar torsion related to this special solution
vanishes. To understand the physical meaning of the constant of integration we
calculate the energy associated with this solution and show how it is related
to the gravitational mass of the system.
