Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Rahu - It represents Illusion, Foreign Lands, Foreign Things (foreign as in unknown things. So, for someone living in Punjab, culture and rituals of Kerala is also unknown and hence Foreign), Drugs, Medicines, any type of intoxication, Fame, Wealth, Success, Obsession, Past-life incomplete Desires, Movies, Television, Online World, Cheating, Imagined Fears, Unusual Things, Unique Things, Creativity, Rule breaker. Rahu also blows things out of proportions. 

House Ruler - Besides these karaka things, Sun & Rahu will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include those things at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas. 

Meaning of Sun-Rahu Conjunction - First thing which strikes in mind with this conjunction is that person is born near Solar Eclipse day of that year. Closer the degrees of Sun & Rahu, closer the person will be to Solar Eclipse during his birth. 1st impact of this planetary position is that person's father may be absent from his life for any reason. Sun is Father and as it is getting eclipsed, it shows that Father is getting eclipsed from person's life. It also means eclipse of Ego and Confidence related thing as generally these things get developed with presence and guidance of Father. Sun & Rahu are bitter enemies. So, Rahu will anyhow impact Sun when they are in same house/sign. It may also create a situation where person may become proud for actually nothing which means false ego got blown-up by Rahu nature. As Sun is Career and Authority, it shows that during early life, these people will have no idea about their right Career. Even if they are in some Career and giving their best, authority will never come to them in early life. As Rahu represents unique, foreign and unusual things, it shows that they will get success and authority by following some unique career or working with Foreign Companies etc. If Sun is in bad dignity, then it shows that person can be prepared to cheat others to gain in career and authority. But if Sun is in good dignity, then it shows that sooner or later Sun will be able to come out of eclipse and person will get authority and name in life through dignified ways.

Who will win the Conjunction? - Rahu matures at 42 years of age. Hence, till 42, Rahu will certainly overpower or eclipse Sun. It will be better after 42 for Sun. But if Sun is in good dignity like in Aries or Leo, then it will be battle of equals. Then Sun will withstand the eclipsing powers of Rahu and will have equal say in this conjunction. Else, it is all Rahu game till 42. 

Dignity & Strength - 

This conjunction will work best in Aries and Leo, as Sun will be in good strength. Then Rahu will explode good qualities of exalted or own sign Sun. It means person can reach high in authority in Govt sector or he can be super creative. In all other signs, Rahu will easily grasp Sun till 42 at least.