What force that cause the moon to drift slowly away from earth .?

Tides but they are balanced in the sense that there are tides from other planets too stabilising it. 

Many of the answers speak of a LOSS of energy which cannot be true.  The earth is spinning and that contains energy.  Due to the effects of the tides this energy is gradually given to the moon INCREASING its energy.  If nothing else changed its orbital velocity would be too high causing it to fling outwards.  So its altitude gradually increases making its gravitational potential LESS NEGATIVE.  ie increasing its energy.  In time the earth will rotate so that one face of the earth always faces the moon and the earth will be spinning at the same rate as the moon is orbiting.  As the moon will be substantially further away then this period would also be a lot longer than the 28 days that it is at present.  So not only is the moon gradually getting further away and the earth is gradually slowing down, the velocity of the moon is decreasing and the period of orbit of the moon is gradually increasing as well.

This is also why one face of the moon always faces the earth.  Being a lot smaller all of its rotational energy has been absorbed by tides within the moon so it doesn't rotate relative to the earth ANY MORE.

You should note that if the moon was revolving around the earth in the opposite direction to the direction of revolution of the earth a) the tides would occur an hour EARLIER each day and b) the tides would cause the moon to lose energy.  To regain balance the moon must go to a lower potential energy by getting closer to the earth. The moon would fall ever closer to the earth.  The final state would depend on the amount of angular momentum of each and of the energy of revolution of the moon versus the energy of rotation of the earth.

Orbital speed of the Moon Vo is constantly slowing down due to friction , therefore :

Vo^2*d = Me*G = costant

If Vo decreases, the distance d must increase !!! 

Gravity and inertia and friction all work together, to cause the moon to drift away. That's because the gravity of the Earth is not directed toward the center of the Earth. It is a little bit off-side, because of the bulge of the ocean tides. That bulge is not directly under the moon, because the spin of the Earth pulls it eastwards.

So the bulge is a bit eastwards of the straight Earth-Moon line, because of the friction of the ocean water against the ocean floor. The moon is pulled a bit toward this bulge, and the pulling force is at a bit of an outward angle from the straight Earth-Moon line.

The tides of the earth, which are caused by the pull of the moons gravity.  The earth and the moon have a complex gravitational relationship, but the tides transfer a little energy to the moon pushing it away.