Polynomials, Cubic Equations and Partial Fractions - Linear and Non-Linear Simultaneous Equations

A positive whole number has two digits which can be expressed as \(10x+y\), where \(x\) and \(y\) are positive integers satisfying \(x>y\). When the two digits are reversed, a new number is formed. The difference between the squares of the two numbers is \(1584\). The sum of the two numbers is \(44\) times the difference between the digits of the original number. Find the two numbers.