We report the first direct measurement of differential transfer cross sections using a Recoil Mass Spectrometer. Absolute differential $1p$ and $2p$-stripping cross sections at $theta_mathrm{c.m.}=180^circ$ have been determined for the system $^{16}$O+$^{142}$Ce by detecting the heavier target-like ions at the focal plane of the Heavy Ion Reaction Analyzer. Focal plane spectra have been compared with the results of a semi-microscopic Monte-Carlo simulation to unambiguously identify the transfer channels. Transmission efficiency of the target-like ions through the spectrometer has also been estimated using the simulation. The methodology adopted in this work can be applied to other recoil separators. The measured excitation functions for the reactions $^{142}mathrm{Ce(}^{16}mathrm{O,}^{15}mathrm{N)}^{143}mathrm{Pr}$ and $^{142}mathrm{Ce(}^{16}mathrm{O,}^{14}mathrm{C)}^{144}mathrm{Nd}$ have been compared with coupled reaction channel calculations. An excellent matching between measurement and theory has been obtained. For $1p$-stripping, major contribution to the cross section has been found to be the transfer of a proton from $^{16}mathrm{O}$ to the $2d_{frac{5}{2}}$ excited state of $^{143}mathrm{Pr}$, leaving behind $^{15}mathrm{N}$ in the $1p_{frac{1}{2}}$ ground state. Transfer of a cluster of two protons from $^{16}mathrm{O}$ to the $2^{+}$ excited state of $^{144}mathrm{Nd}$, resulting in $^{14}mathrm{C}$ in the $0^{+}$ ground state, appears to be the most probable cause for $2p$-stripping. Measured transfer probabilities for $1p$ and $2p$ channels have been compared with Time-Dependent Hartree-Fock calculations. Proton stripping channels are found to be more favourable compared to neutron pick-up channels. However, the theory overpredicts measurement hinting at the need for extended approaches with explicit treatment of pairing correlations in the calculations.
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