Apart from being rater inefficient since the file is imported four times, check the documentation For.

By itself For does not give any output, as is mentioned in the documentation under Details:

You would have to add code to save the results from each row. But it might be easier to use Table instead of For. That would produce an output with the row results in a list.

But wouldn't a loop still be required? (since I want to repeat the same calculation on every row of the spreadsheet)

The functional way to do it is to use Map.

I'm having some difficulty with the map function. Right now my code looks like this:

ClearAll["Global`*"]
e = Import[
   "C:\\Users\\simultaneous_2.xlsx", \
{"Data", 1, {1, 2}, 18}];

x = ToExpression@e;
f = Import[
   "C:\\Users\\simultaneous_2.xlsx", \
{"Data", 1, {1, 2}, 19}];
y = ToExpression@f;
g = Import[
   "C:\\Users\\simultaneous_2.xlsx", \
{"Data", 1, {1, 2}, 20}];
z = ToExpression@g;
h = Import[
   "C:\\Users\\simultaneous_2.xlsx", \
{"Data", 1, {1, 2}, 21}];
m = ToExpression@h;
eq1 = x2 == a + (y2*z2*b)/(1 - b^2);
  eq2 = m2 == b + (y2*z2*a)/(1 - a^2);
fn = NSolve[eq1 && eq2, {a, b}];

So currently x,y,z and m are arrays of length 2. How would I use map on this though? I can't directly map Nsolve because there is no input to that function. I am thinking I would have to use map on x,y,z,m e.g.

x[[i]]=x[[i]]
Map[x, {1, 2}]

but this does not seem to work. Any input would be appreciated

This worked perfectly. Thank you!