Definition
h(p, u) = x(p, e(p, u))
x(p, w) = h(p, v(p, w))
e(p, v(p, w)) = w
v(p, e(p, u)) = u
Or: consider to maximize U subject to budget E, which gives the conditional demand function
Q = F(Price, E)
Note here Q is x, price is the p, and E is w in equations above.
Let U* be the maximum of U, then E is the minimum cost of attaining U*.
E = G(Price, U*)
Where G is the minimum expenditure function.
The CDE function is a special form of G (minimization expenditure function with given U)