x^3-y^3=(x-y)(x^2+xy+y^2)=109(x-y)=218
∴x-y=2
把x=y+2代入x^2+xy+y^2=109,得（y+2）^2+y(y+2)+y^2=109 解得y=5或y= -7
故x=7或-5
故解为（7,5）或（-5,-7）