The ten explorer's equipment had been carefully selected and packed correct the possessive noun?

This is not difficult if you think about the meaning of what you are writing.

The Word 'ten' indicates a plural noun ('ten' is more than 'one'). Therefore the Word following it must be plural: the equipment belongs to ten explorers, not to ten explorer. Therefore the apostrophe must come after, not before, the 's' of 'explorers': 'The ten explorers' equipment had been carefully selected and packed.'