Solving a system of algebraic and transcendental functions

Question

I am attempting to solve a puzzle (LINK). As I have only taken up to multivariable calc, my college course knowledge hasn't helped. How do you solve a system of algebraic and transcendental functions? Do the regular methods of substitutions and elimination work with kinds of functions? I'm not looking for the answer, but would like some pointers in methodologies. The functions are below:

$$ 2936 = \sqrt{U + E + E} $$ $$ 481729 = N + U $$ $$ 22130 = E - O + S $$ $$ 1281959 = S - C \cdot E \cdot U + N^{C} $$ $$ 85450 = C \cdot O $$ $$ 363508 = Olog_{E}N $$ $$ 200350 = \frac{C^{E}}{(S+U)^{C}} $$ $$ 84514 = (\frac{U}{C} - O)! $$ $$ ? = \frac{S}{C} + \frac{N + O + U}{E} $$

Answer 1

You should not solve the equations using regular methods.

Try to think about these few points:

1. The first letters in each of the first 6 equations form the word "UNESCO". Coincidence?
2. The title has the word Journey, what does that tell you?
3. Instead of writing it as 2E, the question says E+E on the first equation. Try to figure out what do the mathematical operations mean here.
4. 6 unknowns, 8 equations, we are given too many equations
5. The word "Long" in the title is written as "Long." and they are using long arrows instead of equal sign. What does the character '.' means? Why long arrows? What does long here refer to?
6. Usually, you assign a value to a variable, but here the direction of the arrow is clearly from a variable to a value. What does this mean?

I hope that helps you.