In this paper, we address a task allocation problem for a robot team that performs a search and attack mission. The robots are limited in sensing and communication capabilities, and carry different types of resources that are used to attack a target. The environment is uncertain and dynamic where no prior information about targets is given and dynamic events unpredictably happen. The goal of robot team is to collect total utilities as much as possible by destroying targets in a mission horizon. To solve the problem, we propose a distributed task allocation framework incorporated with effective resource management based on resource welfare. The framework we propose enables the robot team to retain more robots available by balancing resources among robots, and respond smoothly to dynamic events, which results in system performance improvement.