Multimodal sensing systems have gained widespread adoption in IoT and edge intelligence, due to their ability to collect more comprehensive information of the target, thus improving sensing accuracy. However, this improved accuracy often comes at the cost of increased power consumption and computational overhead. Specifically, sensors require continuous power to collect data, and data processing algorithms not only demand intensive computational resources, but also consume significant energy to analyze the data, hindering the deployment of such systems on the edge. To address this issue, we propose E-M$^{2}$, a framework for efficient multimodal sensing by adaptive sensor-computation activation. First, E-M$^{2}$selectively disables redundant modalities and corresponding data processing modules, effectively reducing unnecessary power consumption and computational overhead. Second, E-M$^{2}$employs an exploration mechanism to reactivate disabled modalities, thus preventing “dead” modalities and enhancing overall system utilization. Finally, E-M$^{2}$conditions the data processing algorithms on the on/standby states of the modalities, thus alleviating the negative impacts of sensor deactivation. Extensive evaluations demonstrate that E-M$^{2}$reduces average power consumption by 40.75% and computational overhead by 48.84% across various sensing tasks, all while maintaining the sensing performance.