Hi,
He found the courage to go outside because he needed to eat / eating.
Which form of 'eat' should be used in this sentence? And why? Or both of them is possible.
Thank you.
...to eat.
The context shows that "He" is fearful of going outside, yet finally did so because of the compelling motivation of needing to eat.
Some have [facetiously?] suggested "... he needed eating", which is to say, he needed to be eaten. That is not logical as it fails to provide the necessary motivation to overcome the fear keeping him inside. Well, unless he has some very peculiar psychology at work; Vorarephilia is a possible, but rather extreme, explanation.
The simplest, most obvious answer is, "...to eat".