Absolutely agree with Karsten Bittkau. Just to add that the case will get even worst if the sample has some scattering due to surface roughness or volume scatterers. Then R=1-T-A-L, where L is the optical losses due to scattering
Generally the transmittance means how much of the sent intensity gets over the system. There are several ways for the missing part (that not get over) to disappear :
absorption, scattering, reflection.
The loss by reflection can be calculated only if you know the amounts of all the other type of losses (absorption and scattering) or you presume that they can be neglected (you think they are 0).
"Can we calculate reflectance from transmission data?" As you can see in most of cases the answer is no.
Actually the answer of "Can we calculate reflectance from transmission data?" is definitely "yes" in the case of transparent sample with smooth surfaces. For absorbing sample the answer also could be "yes". For example if the sample is thin film on known substrate someone can use transmittance data for determination of refractive index, extinction coefficient and thickness of the film and then using the already obtained data to calculate reflectance spectra by well known equations. I personally prefer matrix transfer formalism.
In principle, if you have the transmission spectra you can determine the reflectance. This is true even for a material with absorption. While it seems that you have too many unknowns in A+T+R=1, not all of these quantities are independent. These A, T and R are determined by the complex-valued permittivity of the material, i.e. by two unknown functions of frequency e1(w) and e2(w). This functions are not independent, but are subject to the Kramers-Kronig (K-K) relations (dictated by causality). The issue is a bit complicated though, since K-K relations are not algebraic, but integral: they relate e1 to the integral of e2 over the whole spectrum. But it is doable.
Now practical aspect, there are multiple procedures on how to extract e1 and e2 from you spectra. I recommend fitting your transmission spectrum with a bunch of K-K compliant functions, such Lorentzians. This will yield e1 and e2, then you can calculate your reflectance.
There is a program RefFit that can actually do it. Last time I checked it was free.
I'd suggest to find a spectrophotometer with an integrating sphere, capable to measure diffuse reflectance, and not to rely on formula A+T+R=1. In your case most probably you need to use A+T+R+S=1, where S is scattering. And to measure this parameter, you need either again an integrating sphere or a special scattering measuring instrument.
Recently, an integrating sphere was added to a Shimadzu UV3600 spectrophotometer in our lab, and now we have regularly coming researchers from a friendly lab studying plastics. They measure exactly diffuse transmittance and diffuse reflectance of their (often milky) plastic plates.
If you know the refractive index of your sample, then you can easily calculate the reflectivity using [(n1-n2)/(n1+n2)]^2. if you can calculate the dielectric constant, then you can estimate refractive index n.
If you want to reduce the uncertainty I'll strongly recommend you to measure directly the reflectance (specially in the UV range) if possible and try to avoid easy way.