With the explosive emergence of computation-intensive and latency-sensitive applications, data processing could be envisioned to perform closer to the data source. Similar to edge and fog computing, dispersed computing is considered as a complementary computing paradigm, which can excavate potential computation resources in the network to users, and serve as a supplement for sharing computational burden when the edge is overloaded. In this paper, we first make full use of idle and geographically dispersed computation resources via task offloading, contributing to conserve energy for mobile devices. Specially, a dispersed computing offloading framework concerning the interests of users and networked computation points is proposed. We further transform the initial problem into a multi-objective optimization problem subject to latency and resource constraints. To tackle such a complex problem, an energy-saving bilateral matching algorithm is designed to obtain the optimal task offloading strategy. The simulation results demonstrate that our proposed algorithm can outperform the benchmark schemes in terms of user fairness and can achieve a relatively balanced energy cost ratio. Furthermore, comparative experiments with edge computing are implemented in Amber Response and Disaster Relief scenarios respectively to reveal the advantages of the proposed framework.