How to export images in EPS format that can be opened in CorelDraw

CorelDRAW is not a PostScript viewer. Its ability to import EPS files has serious limitations and is not guaranteed to preserve the original appearance of the figure. One workaround is to place the EPS file inside of the CorelDRAW document instead of importing it but it has a drawback: you will see only EPS preview, not the actual content of the EPS file. (Note that you should Export into "EPS" from Mathematica with option "PreviewFormat" set to anything but None: by default it is set to None and preview is not generated.)

For this in CorelDraw you should create a new document (File ► New...), then place your EPS file via File ► Import... ► (select your file in the "Import" dialog) ► press Import button ► in the "Import EPS" dialog check "Place as encapsulated PostScript" ► press OK. Then you should click inside of the document at any place where you wish to place your EPS file.

Here is how this dialog looks in CorelDRAW X6:

I personally prefer to import EPS file in MS Word which (starting from MS Office 2003) creates its own preview from the PostScript code of the EPS file, and does not use the preview image embedded into the EPS file (which may be absent). In the linked Adobe Community thread and in this answer of mine limitations of the MS Office EPS Import filter are discussed.

Another possibility is to Import the EPS file backward into Mathematica (but it does not always preserve the original appearance of the figure).

The simplest solution of course would be to have something like Adobe Acrobat, GhostScript or free EPS/PS Viewer installed.

I think your syntax is wrong. Try the following

Export[pathWithFileName, mmaImageName, "EPS"], 

where pathWithFileName contains the path and the name of the exported file i.e. "path/filename.eps". In my answer the option "EPS" is not necessarily needed.