We present a detailed study of KIC 2306740, an eccentric double-lined eclipsing binary system. Kepler satellite data were combined with spectroscopic data obtained with the 4.2 m William Herschel Telescope (WHT). This allowed us to determine precise orbital and physical parameters of this relatively long period (P=10.3 d) and slightly eccentric, ($e=0.3$) binary system. The physical parameters have been determined as $M1=1.194\pm 0.008$ M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$, $M2=1.078\pm 0.007$ M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$, $R1=1.682\pm 0.004$ R$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$, $R2=1.226\pm 0.005$ R$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$, $L1=2.8\pm 0.4$ L$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$, $L2=1.8\pm 0.2$ L$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ and orbital seperation $a=26.20\pm 0.04$ R$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ through simultaneous solutions of Kepler light curves and of the WHT radial velocity data. Binarity effects were extracted from the light curve in order to study intrinsic variations in the residuals. Five significant and more than 100~combination frequencies were detected. We modeled the binary system assuming non-conservative evolution models with the Cambridge STARS (TWIN) code and we show evolutionary tracks of the components in the $\log L-\log T$ plane, the $\log R-\log M$ plane and the $\log P-age$ plane for both spin and orbital periods together with eccentricity $e$ and $\log R1$. The model of the non-conservative processes in the code led the system to evolve to the observed system parameters in roughly $5.1 $ Gyr.