  An essential parameter of the Classical Nucleation Theory (CNT) is the
surface energy between a critical-size nucleus and the ambient phase, $\sigma$.
In condensed matter, this parameter cannot be experimentally determined
independently of CNT. A common practice to obtain $\sigma$ is to assume a model
for its temperature-dependence and perform a regression of the CNT equation
against experimental nucleation data. The drawback of this practice is that
assuming the temperature-dependence of $\sigma$ adds a bias to the analysis.
Nonetheless, this practice is common because an analytical solution of the
Classical Nucleation Theory with respect to $\sigma$ is not possible
considering common expressions of this theory. In this article, a general
numerical solution to this problem using the Lambert $W$ function is proposed,
tested, and compared with typical regression methods. The major advantage of
the proposed method is that there is no need to assume a model for the
temperature-dependence of $\sigma$.
