In this paper, we study a general transactive energy (TE) retailing problem in smart grids: a TE retailer (e.g., a utility company) publishes the energy price, which may vary over time. TE customers arrive in an arbitrary manner and may choose to either purchase a certain amount of energy based on the posted price, or leave without buying. Typical examples of such a setup include a transactive electric vehicle charging platform, or a general market-based demand-side management program, etc. We consider the setting where the customer arrival information is unknown (i.e., without prediction), and focus on maximizing the social welfare of the TE system through a posted-price mechanism (PPM) that runs in an online fashion with causal information only. We quantify the performance of the proposed PPM in the competitive analysis framework, and show that our proposed PPM is optimal in the sense that no other online mechanisms can achieve a better competitive ratio. We evaluate our theoretic results for the case of transactive electric vehicle charging. Our extensive experimental results show that the proposed PPM is competitive and robust against system uncertainties, and outperforms several existing benchmarks.