The cracks spanned over the screen's upper surface like tendrils, white and glossy in appearance.
Does the phrase white and glossy in appearance modify the word 'tendrils', or the word 'cracks' and 'spanned'?
It does not seem to be a very well written sentence. "Spanned over" should be "spanned." Technically, "white and glossy" should modify "tendrils," but I suspect that it is intended to modify "screen."
Here is what I am guessing was intended.
The screen, spanned by tendrils of cracks, looked white and glossy.
LATE EDIT DUE TO OP's COMMENT & JASON BASSFORD'S EXCELLENT ANSWER
If what was intended was to modify "tendrils," the common positioning of the adjectives would be before the noun modified. It is permitted in certain circumstances to put adjectives after the noun modified, especially when the adjective itself is modified by a prepostional phrase. For example, it is not good English grammar to say "He picked up a sheet red," but it is good grammar to say "He picked up a sheet red with blood."
Now this is opinion about prose style, but I think your original sentence was hard to interpret because "in appearance" does not really modify "white" or "glossy," terms which are by definition about appearance. So your intended meaning could easily have been rendered as "glossy, white tendrils." By changing to a grammatically questionable word order with a redundant prepositional phrase, the reader stops to decipher what is really being said and then wonders whether the intended meaning is the same as the grammatically correct meaning. It is why I like a spare style.
To paraphrase a comment (note that the existing answer is a perfectly correct interpretation in terms of what was actually asked):
How can I rewrite the sentence in my question so that white and glossy (unambiguously) modifies tendrils?
You could try something like this:
The cracks spanned the screen's upper surface like white and glossy tendrils.