Utilization of abundant measurements provided by supervisory control and data acquisition (SCADA) system has attracted increasing attention. Real-time estimation of transmission line parameters, utilizing voltage and power flow measurements provided by remote terminal units (RTUs) located at two substations across the line, has been investigated, recently. This paper improves this approach by introducing a novel exact linear reformulation of the problem, which can be solved in closed form. The distributed-parameter model of long transmission lines is considered and its parameters are estimated in a noniterative manner using RTU measurements. The method is also extended to estimate transformer series impedance and tap position by SCADA measurements, linearly. As such, the disadvantages associated with the previous iterative approach, e.g. concern over convergence, for transmission line parameters are avoided. Moreover, the novel technique for estimating transformer parameters allows to determine the tap position as well as updated transformer series impedance. Furthermore, a thorough analysis is presented to take the measurement accuracy into account. Simulation results for different transmission lines and transformers in the IEEE 118-bus test system are reported, where the result indicate successful performance of the proposed algorithms.