"The words "is -9" is the right side of the equation and on the end
of the equation will be " = -9"

Now we'll do the left side of the equation:

"X more than Y"  means "Y+X"

So 

"one more than the difference between 18 and seven times a number is -9

is a case of "X more than Y", where

X = "one",  and

Y = "the difference between 18 and seven times a number"

So Y + X = "the difference between 18 and seven times a number" + "one"

or using the number 1 instead of the word "one":

So Y + X = "the difference between 18 and seven times a number" + 1

-----

Next, "The difference between Z and W"  means Z-W, where

Z = 18 and W = "seven times a number"

So Z-W = (18-"seven times a number")

So far we have 

Y + X = ("the difference between 18 and seven times a number") + 1

So far we have

"18-"seven times a number" + 1

----------------------------

"X times Y" means X∙Y

So "seven times a number"  means "7 ∙ a number"

So far we have:

("18-"seven times a number") + 1 which means

("18-"7 ∙ a number") + 1

-----------------------------

"a number" means the unknown variable, say N

So far, we have 

("18-"7 ∙ a number") + 1

which becomes:

("18-"7 ∙ N") + 1 or 

"(18-7N) + 1" 

And finally we put on the right side " = -9 "

(18-7N) + 1 = -9

Edwin