I think you ought to search CPAN for code to do a least-square curve fit. Perhaps Algorithm::CurveFit or Statistics::LineFit. Since you want a simple scale factor, then you're looking at fitting a line. So you'd minimize the value of sum(F(k))=(E1k-A*E2k)^2, where E1 is your first column, E2 is your second column, and A is your scaling factor.
Disclaimer: My numerical analysis course was over 25 years ago, so my memory may be a little off. You'll want to double-check me, in case I've inadvertently missed (or added) something...
...roboticus
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