But can you even express this function with the elementary operator symbols, exp, log, power and trig functions? It seems to me like no, you can't express "largest real solution" with those (and what's the intended result for complex inputs?)

At least eml can express the quintic itself, just like the above mentioned operators can

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tliltocatl 2 days ago | parent [-]

Author and EML are using different definitions of elementary functions, EML's definition being the school textbooks' one (polynomials, sin, exp, log, arcsin, arctan, closed under multiplication, division and composition). The author's definition I've never met before, it apparently includes some multi-valued functions, which are quite unusual.

	▲	reikonomusha 2 days ago \| parent [-]
		Wikipedia says: > More generally, in modern mathematics, elementary functions comprise the set of functions previously enumerated, all algebraic functions (not often encountered by beginners), and all functions obtained by roots of a polynomial whose coefficients are elementary. [...] This list of elementary functions was originally set forth by Joseph Liouville in 1833. which seems to be what the blog post references.