We construct an approximate solution to the equation of energy spectrum balance for developed homogeneous isotropic turbulence in the dissipative range. This equation is closed in the framework of the statistical model we use. The model is based on the principle of maximum randomness, renormalization group technique, and epsilon-expansion. We calculate the energy spectra and the transfer functions in the cases where the wave numbers relate to the energy-containing and inertial ranges. The Kolmogorov constant is found to be C-K = 1.55. It is shown that the one-dimensional longitudinal energy spectrum calculated without any free fitting parameters and normalized in von Karman-Hovart energy units, is in good agreement with experimental data on decaying turbulence.