Numbers...without numbers?

Consider a positive four digit number, $\overline{ABCD}$ .

Where:

$A + B + C + D = \overline{AD}$

C - B = A

$\overline{AD} \times \overline{ DA} = \overline{ABCD}$

What is number $\overline{ABCD}$ in its numerical representation?

Details and assumptions. Each letter represents one numerical digit. ABCD is positive. AD is equivalent to 10A +D, not AxD.