She was beside herself with anger.

Literal

She [topic-は] anger [by-で] self [object-を] forgot.

我を忘れる ('to forget oneself') is a set expression meaning to lose one's composure or become beside oneself. 我 (われ) is a classical/literary word for 'self.' The English idiom 'beside oneself with anger' maps remarkably well to this Japanese expression, though the metaphors differ — Japanese focuses on forgetting the self, English on being displaced from it.