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.