For Epicurus, well-being can be obtained by knowledge, friendship, and living a virtuous and temperate life. He advised the enjoyment of simple pleasures, by which he meant abstaining from being enslaved by bodily desires, such as sex and appetites. This doesn’t mean being celibate or ascetic, but it does mean giving each pleasure its proper place in your life, neither exalting it as a dire necessity nor denying it entirely.
Zeno pursued the same kind of well-being as Epicurus; but he focused more on overcoming the barriers to it, whereas Epicurus was interested in the active causes of it. Zeno argued that certain ways of looking at the world – craving fame, for example, or requiring that things must always go your way – are pretty much guaranteed to cause anxiety, depression and anger. His method paid attention to how you could learn to think more rationally.
Between them, Stoicism and Epicureanism give a rounded picture of how to achieve a good life; what you need for fulfilment, and what you should avoid if you want to be at peace with yourself and the world.
Three hundred years before Zeno and Epicurus got going in Athens, India saw the rise of a similar (but, of course, characteristically Indian) philosophy. Its core idea was that, while dissatisfaction is universal, its cause can be known and its cure can be attained. Like Stoicism it advocated putting aside the excessive demanding for things to go well, and replacing it with calm acceptance. It also promoted the discipline of mindfulness, which resembles the Stoic method of “staying the appearances”.
For these reasons we consider Buddhism to be an important inspiration for Epicurean Humanism. We don’t need to adopt every aspect of it, such as a belief in literal reincarnation or karma: we can quite happily cherry-pick what fits with the rest of our philosophy.