Divergence theorem(problem with boundaries)

Question

I am struggling with a problem: I have vector function such that: $$\vec{W}=[x-z,y,z+1] $$ and surface specified by two functions: $$z=\sqrt{x^2+y^2} $$ $$z=6-x^2+y^2$$ So this is basically enclosed surface over a vector field. Knowing that we can use a divergence theorem since:$$\vec{W}\in{C^1}(U)$$ $$U\supset S(=\partial{\bar{V}})\cup V$$ Where: $$\bar{V}={[(x,y,z)\in R^3:\sqrt{x^2+y^2}\le z\le 6-x^2+y^2:(x,y)\in \bar{D}]}$$ But I have no idea how can I get area D, which will be needed for integrating.How can I find intersection between cone and a hyperbolic paraboloid ?