In many scientific papers, the article before the word "Equation" is omitted. Is there any grammar statement behind this? For instance:
"Equation (8) contains various approximations, and we have to check their consistency."
Your example refers to a specific equation, namely equation 8, therefore the equation eight or an equation eight would not really make sense in this case. An Equation y=x^2 however is a perfectly valid thing to say.
Try thinking of "Equation (8)" as the name (identifier) of the equation, just as your name (identity) is "freude".
You would expect someone to refer to you just by your name, as "freude" - you wouldn't expect them to refer to you as "the freude". Similarly, you refer to Equation (8) as "Equation (8)" because that is its name.
The definitive article has its use when constructing an argument wherein a second / tertiary equation forms a lemma that contrasts other lemmas in the argument.
The definitive article can thus be used to create contrast between the facets of the argument.