In 2000, Kulish and Lage proposed an elegant method, which allows one to obtain analytical (closed-form) solutions to various energy transport problems. The solutions thus obtained are in the form of the Volterra-type integral equations, which relate the local values of an intensive property (e.g., temperature, mass concentration, velocity) and the corresponding energy flux (e.g., heat flux, mass flux, shear stress). The method does not require one to solve for the entire domain and, hence, is a non-field analytical method. Over the past nineteen years the method was shown to be extremely effective when applied to solving numerous energy transport problems. In spite of all these developments, no general theoretical justification of the method was proposed until now. The present work proposes a justification of the procedure behind the method and provides a generalised technique of splitting the differential operators in the energy transport equations.