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

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/

There are several methodolgies. See for instance,

Nolis, P.; Roglans, A.; Parella, T. IFSERF, an isotope-filtered SERF experiment for the precise measurement of proton-proton coupling constants between chemically equivalent protons. Journal of Magnetic Resonance. 2005, 173, 305-309.

also references therein.

For overlaped signals, you can use some experiments to solve this problem. One is the use of the technique CSSF where signals overlap with at least 2 Hz separation between them using selective excitation (ref.:P.T. Robinson et al., In phase selective excitation of overlapping multiplets by gradient-enhanced chemical shift selective filters. Journal of Magnetic Resonance 170 (2004) 97–103 link text). The other is the use of SELINCOR technique (1D version of HMQC experiment). Irradiatin the olefinic carbon, you will obtain the 1H spectrum via 1J CH correlation. (REF.: S. Berger., Journal of Magnetic Ressonance 81 (1989), 561-564 link text)