Although digital cameras can acquire high-dynamic range (HDR) images, the captured HDR information are mostly quantized to low-dynamic range (LDR) images for display compatibility and compact storage. In this paper, we propose an invertible tone mapping method that converts the multi-exposure HDR to a true LDR (8-bit per color channel) and reserves the capability to accurately restore the original HDR from this {\em invertible LDR}. Our invertible LDR can mimic the appearance of a user-selected tone mapping style. It can be shared over any existing social network platforms that may re-encode or format-convert the uploaded images, without much hurting the accuracy of the restored HDR counterpart. To achieve this, we regard the tone mapping and the restoration as coupled processes, and formulate them as an encoding-and-decoding problem through convolutional neural networks. Particularly, our model supports pluggable style modulators, each of which bakes a specific tone mapping style, and thus favors the application flexibility. Our method is evaluated with a rich variety of HDR images and multiple tone mapping operators, which shows the superiority over relevant state-of-the-art methods. Also, we conduct ablation study to justify our design and discuss the robustness and generality toward real applications.