Optical birefringence and calorimetric studies have been conducted with respect to structural relaxation of E-glass (a type of calcium-alumosilicate glass system) fibers. Upon fiber drawing, the liquid of E-glass is thermally hyperquenched and mechanically stretched. Hyperquenching (cooling rate >10(6) K/min) leads to higher enthalpy state of liquids, and thereby, to a higher fictive temperature than normal quenching (20 K/min), whereas stretching results in structural anisotropy of glasses, i.e., a certain degree of preferred structural orientation (stretched network) along the axial direction of the fibers, which is quantified by the optical birefringence. Simultaneous relaxation of both anisotropy and excess enthalpy (relative to the enthalpy of a glass cooled at the standard rate of 20 K/min) upon static annealing and dynamic heating is observed, both of which can be described using the Kohlrausch function. However, there is a striking difference between the birefringence and the excess enthalpy relaxations. The birefringence decays much faster than does the excess enthalpy during annealing. These observations imply that the birefringence decay results from fast relaxation of the local structure, while the enthalpy relaxation results from slow relaxation of larger domains of the network.