Looking at the Society of Genealogists' online data, the marriage appears to be listed in Boyd's Marriage Index, with a reference to the Faculty Office Marriage Licences. I'm not sure how much of this a non-member would be able to see.
Anyway, I suggest that first of all you try to find if Boyd's Marriage Index is online anywhere else, to confirm what I've found.
(earlier comment on content of Boyd's index deleted)
Next you'd need to contact the SoG for a digital copy of any or all of the licence, bond or allegation. You don't need to be a member for this - see
https://societyofgenealogists-shop.myshopify.com/collections/digital-copy-serviceAs far as I could tell, the only information you'd need to place an order is the names and year.
ADDED:
From looking a bit further, it appears that the SoG might only have copies of the licences from 1701 onwards. Before placing an order and paying for it, I suggest you contact them as per this page:
https://societyofgenealogists-shop.myshopify.com/pages/digital-copy-serviceto check whether they have the one you want, and if not, where you might be able to get a copy.