This might not strictly meet the requirements since I did make use of the abs() function, I'll let you guys decide.

#include
#include
int main(int argc, char *argv[])
{
float argument = atof(argv[1]);
float guess = argument;
float oldguess = 0.0;
float tolerance = .0000000001;
int cnt = 0;
float temp = guess - oldguess;
while (abs(temp) > tolerance)
{
oldguess = guess;
guess = ( oldguess + ( argument / oldguess ) ) / 2.0;
cnt++;
temp = guess - oldguess;
}

std::cout << "Square root of " << argument << " is approximately " << guess << std::endl;
std::cout << "Derived in " << cnt << " iterations." << std::endl;
}