Step 1 :We have two equations here: \(x + y = 19\) and \(x - y = 5\). We can solve these equations simultaneously to find the values of x and y.
Step 2 :Solving the equations gives us the solution: \(x = 12\), \(y = 7\)
Step 3 :Final Answer: The two numbers are \(\boxed{12}\) and \(\boxed{7}\)