Dene is an annoying word that comes up occasionally in archaic writings with any number of alternative meanings and spellings.
Dene is often a component of place names. It is perhaps most common as a variant of 'dean', meaning a wooded vale; this is the form used in Jesmond Dene and Dene park. Alternatively, a dene, den, deine, or deane is a bare sandy spot by the sea, or possibly, a low sand hill, as in Deneside in Seaham or the North Denes in Great Yarmouth. It may also be used more generally to refer to marshlands near the sea; however this is particularly used in the phrase 'Den and Strand' (or 'Denne and Strand') in reference to the marshes around Great Yarmouth, and is not often seen spelled 'dene'.
Even more archaic, dene was a recurring eggcorn of the 1300 and 1400s (the OED calls it a "fictitious sb."). It arose from the grammatically incorrect division of the word bedene (often written as 'bydene'), splitting it into 'by dene'. The dene might then be used apart from the 'by', most often in the phrase 'with dene'. Bedene is another annoyingly vague word, meaning, depending on context, 'together', 'completely', 'sometimes perhaps', 'continuously', or 'in a little while'.
And very occasionally, dene could also be used to mean ten.