If the height of the flagpole is x meters, then the length of the rope is (x+ 1) meters.

In Rt△ACE, AC=x meters,

AE=(x- 1) m，ce = 8m，

According to Pythagorean theorem, (x- 1)2+82=(x+ 1)2,

Solution: x = 16.

Answer: The height of the flagpole is16m.