Your AddNumber class interacts with the console, so it doesn't matter where it is called, it will do just that. You're on the right path though for making your JTextArea resemble a console. Before tackling this problem, think about what the console does. For example, it can take in lots of input at once and process it. Likewise, it can output lots of data at once. You're going to have to use some form of I/O, such as an InputStream, OutputStream, BufferedReader, BufferedWriter, PipedInputStream, etc... . Next, you're going to have to tell your compiler that it should re-direct standard output from the console to a custom I/O. This can be done using the method System.setOut(PrintStream stream), where stream will encompass whatever I/O you've chosen. Similarly, you'll do the same for take in information using System.setIn(InputStream inStream). Next, you're going to have to override event listeners so when you press Enter, it will take in/print out information and move to the next line.
The second last step would be to make sure your program will constantly execute. You can use a Thread for this or a SwingWorker (similar to a Thread but designed for javax.swing components, which is what you're using).
The last step would be to adjust the fonts, background colour, foreground colour and make it look like a console.
Overall, if I were you, I'd start on something simpler and work your way up to this.