A technique facilitates use of a packer in a borehole or within other tubular structures. The packer may be constructed with a tubing, a metal sealing element mounted around the tubing, and a differential pressure valve system. The metal sealing element may be expanded under fluid pressure for sealing engagement with a surrounding wall surface. Additionally, the differential pressure valve system is placed in fluid communication with the interior of the metal sealing element and comprises a plurality of valves which operate automatically to increase pressure within the metal sealing element when certain pressure differentials occur. The differential pressure valve system enables the packer to hold against higher differential pressures and also may be constructed so the packer is less sensitive to thermal variations.