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My father was a swordsman who used the dual long-blade style. Before my father's execution...My brother and I were each entrusted with one blade.


Would you tell me what part of speech "each" is in the sentence?

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An adverb.

Each is also an adverb. The children were given one each, handed to them or placed on their plates. They were selling tickets at six pounds each.
(Collins)
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I'd say it's a 'determinative'.

Generally, determinatives belong in the subject NP, such as in "We each took a card", where "each" quantifies over "we" in the noun phrase "we each".

However, certain determinatives that are semantically associated with the subject, such as "each", "all", and both", can be positioned outside the noun phrase, as in your example, where it is located after the auxiliary verb "were".

Its function is that of 'adjunct'.