Let's break down the problem step by step:

• Initially, there is enough food for 1000 soldiers for 30 days.
• After 10 days, 1000 soldiers join, so the total number of soldiers is now 2000.

First, we calculate how much food is used in the first 10 days for 1000 soldiers:

Food used in 10 days = $1000 \times 10 = 10{,}000$ soldier-days of food.

Since the total food available is enough for 1000 soldiers for 30 days, the total amount of food available is:

Total food = $1000 \times 30 = 30{,}000$ soldier-days of food.

After the first 10 days, 10,000 soldier-days of food have been used, leaving:

Remaining food = $30{,}000 - 10{,}000 = 20{,}000$ soldier-days of food.

Now, with 2000 soldiers in the garrison, we calculate how many days the remaining food will last:

Number of days = Remaining food / Number of soldiers = $\frac{20{,}000}{2000} = 10$ days.

Therefore, the soldiers will be able to carry on with the remaining food for:

10 days.