Adrian,
Welcome to the world of Lionel model trains!
To operate more than one train on the same track, you need to use a Command system, such as the Lionel Legacy system:
http://www.lionel.com/products/990-legacy-command-set-6-14295Your second engine would need to be Command Controlled. The Legacy system will allow you to operate one non-command locomotive (what you have, also known as a "Conventional" locomotive), and one Command Controlled loco (or multiple Command Controlled locomotives).
Larry