He gave her an engagement ring and they differed as to whether it was a gift or a loan

Firstly: 

With regard to the gifts that the husband gives to his wife – including the engagement ring if it is not regarded as part of the mahr – it is permissible for him to take them back and to ask for them when divorce occurs, if the divorce is initiated by her. 

This is the most correct view according to the fuqaha’ and it is the view of the Maalikis according to one opinion. It is also the view favoured by Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) and he attributed it to Ahmad (may Allah have mercy on him). 

The Hanafis, the Maalikis according to the other opinion, and the Shaafa‘is are of the view that the husband may take back his gift if the actual gift still remains, whether the annulment came from the husband or from the wife. 

See: al-Fataawa al-Kubra, 5/472; al-Sharh al-Sagheer, 2/348; al-Durr al-Mukhtaar ma‘a Haashiyat Ibn ‘Aabideen, 3/153; Tuhfat al-Muhtaaj, 7/421; Sharh Muntaha al-Iraadaat, 3/24. 

The basic principle is that it is haraam to take back gifts and presents, because of the reports which condemn that and forbid it, such as the report narrated by Abu Dawood (3539), al-Tirmidhi (2132), al-Nasaa’i (3690) and Ibn Maajah (2377) from Ibn ‘Umar and Ibn ‘Abbaas from the Prophet (blessings and peace of Allah be upon him) who said: “It is not permissible for a man to give a gift or a present then take it back, except in the case of what a father gives to his son. The likeness of the one who gives a gift then takes it back is that of a dog that eats then when it is full it vomits, then it goes back to its vomit.” This hadeeth was classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

But an exception from that is made in the case of a gift that the giver gave in return for something, such as in the case of marriage, because it was not given purely for nothing, so if he does not achieve his aim, it is permissible for him to take back his gift. 

Based on that, if we assume that you gave this ring to your fiancée then the divorce came from her side, in that she asked for divorce or there was something on her part which meant that you could not stay with her, such as her neglecting the prayer, then you have the right to take back what you gave to her. 

Secondly: 

If you did not give the ring as a gift, rather you gave it to her as a loan that she was to give back to you after the party, if she believed you with regard to that then she has to give it back to you. But if she disputed with you concerning it, then what counts is your word plus your oath, i.e., you should swear that you gave the ring to her as a loan and not as a gift. 

It says in Haashiyat Ibn ‘Aabideen (5/710): A man bought some jewellery and gave it to his wife and she used it, then she died and the husband and her heirs differed concerning it, whether it was a gift or a loan. What counts is the husband’s word plus his oath that he gave it to her as a loan, because he is denying that it was a gift. End quote. 

See also: al-Fataawa al-Hindiyyah, 4/399 

One of the principles mentioned by the fuqaha’ is: if the receiver and the giver differ concerning a gift, what counts is the word of the giver. This was mentioned by al-Zarkashi (may Allah have mercy on him) in al-Manthoor fi’l-Qawaa’id (1/145) who mentioned an example of it: 

If he gives some dirhams to his wife and says: I gave them to her as part of the dowry, and she says: No; rather it was a gift, what counts is the word of the giver. Al-Raafa‘i narrated this in Kitaab al-Sulh from our companions. And it says in Kitaab al-Sidaaq: If the spouses differ with regard to some money that was given by one to the other, and he says, I gave it as part of the mahr and she says, Rather it was a gift, what counts is his word plus his oath. End quote. 

If you swear that you gave her the ring as a loan and not as a gift, then she has to return it to you. 

And Allah knows best.