How to solve this word problem

If a number is subtracted from 31, the principle square root of this difference is equal to the number decreased by 1. Find the number(s)

let's break it down a tiny piece at a time.

If a number: what number? I don't know, so let's give it a name. How about N? You can use any name you want, but I assure you it's more convenient to use N than to use Rumpelstilzchen.

If N is subtracted from 31: well that's just 31-N

the principle square root of: square root function gives two answers, one positive and one negative but both have the same magnitude. for example square root of 4 is +2 and -2. 2*2 is 4 and so is -2*-2. the principle solution is the positive one.

this difference: difference is the result of a subtraction. which subtraction? we'd only mentioned one so far, which is 31-N. and the square root is of this. so now we have this expression for all the words covered so far:
sqrt(31-N)

is equal to: that's just an = sign. so we're going to form an equation. everything said before the = goes on one side and everything said after it goes on the other side.

the number decreased by 1: we're calling the number N, so this is just N-1 since subtracting 1 from N decreases it by 1. And now we have the full equation:

sqrt(31-N) = N-1

to eliminate the sqrt function we can undo it by squaring both sides

31-N = (N-1)^2

expand the right hand side

31-N = N^2 -2N +1

add N to both sides and subtract 31 from both sides
0 = N^2 -N -30
I'll just swap things around for convenience
N^2 -N -30 = 0

this easily factors
(N-6)(N+5) = 0

so two possible solutions are N=6 and N=-5

but in our original equation, we are wanting the principle sqrt
sqrt(31-N) = N-1
that means the left hand side is a positive number. if the left hand side is positive, so must the right side because of the equal sign