The ¹⁷F(p,γ)¹⁸Ne reaction plays an important role in various astrophysical processes. However, direct measurements of (p,γ) reactions involving radioactive nuclei will remain difficult even at cutting-edge facilities in the near future. As a result, there is a need to develop reliable alternative methods to obtain the relevant information for understanding these reactions. The (d,n) proton transfer reaction is well-suited for studying the (p,γ) reaction due to the low Q-value at the proton threshold and the less complicated transfer mechanism when compared to similar transfer reactions. Because neutrons are neutral particles and thereby difficult to detect, very few attempts have been made to study the (d,n) reaction using radioactive ion beams. Here, I describe the development of a compact neutron detector array, RESONEUT, that is specialized for detecting the low energy neutrons from the (d,n) reaction in inverse kinematics. The efficiency properties of the detectors are characterized in a stable-beam test experiment by detecting the low energy neutrons from the ¹²C(d,n)¹³N reaction in inverse kinematics. The detectors are then used in a radioactive beam experiment studying the ¹⁷F(d,n)¹⁸Ne reaction at the RESOLUT facility. Our results confirm that the 3+ state at E[subscript R]ٖ = 599.8 keV is the lowest lying l=0 proton resonance and no additional states were observed. We have also succeeded in measuring the transfer spectroscopic factors of the 2₂+ bound state by detecting neutrons from the transfer reaction. The results are consistent with the spectroscopic factors measured from the mirror reaction, ¹⁷17O(d,p)¹⁸O, but inconsistent with the spectroscopic factors measured in the ¹⁷O(p,γ)¹⁸F reaction by Rolfs[Nucl. Phys. A217, 29 (1973)]. As a result, the direct capture contribution to the reaction rate, previously calculated by Garcia et. al[Phys. Rev. C43, 2012 (1991)] using spectroscopic factors from Rolfs, will need to be revised.