In Romans 9 Paul details the doctrine of election and reprobation. Now here in Chapter 10:12-13, he seems to go out of his way to explain that salvation is available to all who call upon the name of the Lord. Is Paul turning his back on what he just declared in Romans 9? Some believe that Paul is teaching two contradicting truths – but this cannot be so. In truth, God sovereignly elects those who will be saved; however, all who come to Him, must call upon His name and proclaim Him as their savior by repenting of their sins. Be sure that while it may appear so to our finite minds, the Bible never contradicts itself.
Having said this, Romans 10 is not teaching the universal offer of the Gospel. The context set by Romans 9-11 has Paul teaching his fellow countrymen that this Gospel makes no distinction based on race. This idea is reiterated throughout the book of Romans (Ro 1:16, 2:11-14, 3:10-18, 3:29-30, 4:9-12, 5:18-19, and 9:24). There are no human differences that exclude a people from the Gospel for whosoever shall call on Him will be saved.
