Purpose of writing this paper is to solve a transcendental  function containing product of a variable and its double exponential by a  unique method of approximation. If the value of the said product is given, then its inverse function is approximated by use of linear expression in place of natural logarithm of a positive real quantity and that transforms the function to a quadratic equation. Roots of the equation are, then used for solving the function. For precise approximation, the process is iterated a number of times and more the number of iterations, more precise will be the approximation. To prove precision of the formulae derived, a number of examples are given in tabular form.