Not your average table of operations

Consider the 10-digit integer

\(N=\overline { ABCDEFGHIJ} \)

(where \(A,B,C,D..J\) are the digits of \(N\)). Each digit of \(N\) is a number between \(0\) and \(9\) inclusive and all digits of \(N\) are different from each other.

What must be the value of \(N\) so that the three vertical and three horizontal operations in the table below are correct?

\(\begin{matrix} \overline { EDJH } & \div & \overline { JF } & = & \overline { AA } \\ - & \quad & + & \quad & + \\ \overline { EDB } & \times & \overline { I } & = & \overline { EHCG } \\ \quad = & \quad & = & \quad & = \\ \overline { EEID } & - & \overline { DJ } & = & \overline { EEAE } \end{matrix}\)

Details and assumptions

You may assue that only one value of \(N\) satisfies the constraints above.

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