The woman, who lives alone, was visited by the two men who offered to clean her guttering for £10.
Once up the ladders, the males removed six roof tiles and informed her that her roof was damaged and leaking and said they would need £250 for materials to fix it.
The victim went upstairs to get the money and paid them.
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The two suspects later returned and asked the victim for a further £100 which was again paid in cash.
One of the males asked her to follow him outside and look at the roof, but while doing this the second male sneaked inside the house.
On realising what had happened the victim returned indoors and saw the second male running down the stairs.
Both males got into a small white van, stating they were going for more materials, but have never returned. The incident happened on Saturday, May 2.
The contact phone number given goes straight to voicemail They are described as white males and were both wearing black gloves with red grips.
The first man was around 5ft 7, approximately 35 years-old with slim build and short thick black hair wearing a grey tracksuit top, black trainers and blue jeans.
The second was around 45, a large build with short light brown hair,and wearing a black leather jacket, blue jeans and trainers.
A police spokesman said: “Not only have they stolen £360, but they have also left the victim with a damaged roof and feeling very stressed and frightened.
“Please remind elderly relatives, neighbours and friends about this type of scam as, due to the time of year, when people start to think about property maintenance, these bogus workmen may prey on the vulnerable and try to obtain cash, through deception, for roofing work that is not necessary.