Answer: I would use Compromising conflict resolution style
Step-by-step explanation:
Since Both of the parties have equal power,lack trust/openness for problem solving
and they are both under time pressure to resolve the conflict which means as a manager I would use COMPROMISING CONFLICT RESOLUTION STYLE reason been that this type of conflict resolution style would enable me find a solution that will partially please both of the parties and to help encourage both of the parties involve in the conflict to give in some points about the conflict which will inturn help me to balance the needs of both of the parties.