Are certain logP values eluted when 100% methanol is used as the solvent in a C18 column?
HPLC is often used to determine lipophilicity in industry, as the original methods to determine logP by partitioning between octanol and water was not particularly amenable to high-throughput assay. 

Lipophilicity values measured by HPLC are often reported as cLogP / cLogD (where c is relating to the fact that the value has been determined by some form of chromatography). 

Experimentally, a C18 column is used with an acetonitrile/water solvent system, buffered appropriately. Unlike with the octanol/water procedure, different companies run these HPLC assays differently, and as such they aren't as comparable (i.e. if you ran 20 compounds through a GSK assay, and the same 20 compounds through a Pfizer assay, the precise values for cLogD obtained in each case would vary, even if the general trend remained the same).

In terms of you doing this yourself, you'd first need to find a training set of compounds with known and reliable values. If you know paracetamol comes of at x mins and has a  literature logP of y, and ibuprofen comes off at z mins and has a literature logP of w, you can interpolate. When you then run an unknown sample, its retention time using your method can be used to predict the cLogP/D (keep in mind that you'd need a far greater training set than 2 compounds).