It will be quite impossible to separate both solvents by an extraction method; both are miscible with water and organic solvents.
The suitable way to separate them is by fractional distillation; the boiling point of THF is 66 C and that for ethyl acetate is 77.1 C (difference of 11.1 C).
Fractional distillation is the separation of a mixture into its component parts, or fractions, separating chemical compounds by their boiling point by heating them to a temperature at which one or more fractions of the compound will vaporize. It uses distillation to fractionate. Generally the component parts have boiling points that differ by less than 25 °C from each other under a pressure of one atmosphere. If the difference in boiling points is greater than 25 °C, a simple distillation is typically used.
Ethyl acetate (EA) is less soluble (8.7g/100g) in water than tetrahydrofuran (THF, solubility 100g/100g) see link. Repeated extractions with water should allow for the removal of most of the THF from the ethyl acetate.
Would it be possible to describe in detail how you are going to make the extraction in the lab and what is the organic phase that you are going to use?
If you use a long column in the fractional distillation the chances to get a separation will be very high. Additionally, if the last fraction still contains both solvents, you can re-distill this fraction.
Please note that petroleum refineries use distillation to separate crude oil where the difference in boiling points between the components is smaller than in your case.
I believe that using a long column will solve the problem.
For vapor-liquid equilibrium data on the tetrahydrofuran - ethyl acetate system, see: H.S. Wu, S.I. Sandler, "Vapor-liquid equilibria of tetrahydrofuran systems", J. Chem. Eng. Data, 33(2) 1988, pp. 157–162; http://pubs.acs.org/doi/abs/10.1021/je00052a030
I would extract the ethyl acetate:THF mixture directly 3 or more times with water containing between 1 and 3M NaCl to remove the THF from the ethyl acetate. I would use at least 25% of the total volume as the volume of aqueous phase. You will have to experiment to see what concentration of salt and what aqueous:organic ratio is best for the extraction.