It is not clear whether if the overlap included the hydrogens directly attached to the double bond. If the protons attached to the double bond have well resolved resonances then the measurement of the coupling constant between these two hydrogen nuclei will allow you to distinguish the E and Z isomers. The trans isomer is expected to have a much larger coupling constant.
However, if the resonance overlap involves the resonances of the hydrogens directly attached to the double bond in R1-CH=CH-R2, then a spectral simulation and fitting program such as LAOCOON/PERCH may allow you to extract the relevant coupling constant.
A few relevant references are listed below:
J. Chem. Educ., 1990, 67 (3), p 235; Matthew Clark and Joseph S. Thrasher; LAOCOON PC: NMR simulation on a personal computer
You may want to take a look at LAOCOON3: Organic Magnetic Resonance Volume 13 Issue 4, Pages 277 - 278
http://www.perchsolutions.com/products/PERCHNMRSoftware.html.
A list of NMR software is available at http://www.spincore.com/nmrinfo/
Organic Magnetic Resonance Volume 13 Issue 4, Pages 277 - 278
